Thanks for taking the time to cover these higher-level topics. I know they don't perform as well as some of your lower-level videos, but this is incredibly helpful to college-level students such as myself whose professors glossed over most of this information.
@@boredscientist5756 which is why they said "higher-level" and not high-level, as in comparing to other videos in the channel. Check your logic and understanding of language before you criticize what people may find challenging or high-level.
Professor Dave, I can’t thank you enough for all the effort you put into making this content. I can assure you it‘s been very helpful for students all over the world ! I‘ve recently started a quantum chemistry course at university and came to understand it better after watching your series. If you are interested, please make a video on experimental application of quantum mechanics (for example, Hartree-Fock approximation) or elaborate on various interpretations of quantum mechanics (I find the many-world interpretation particularly mind -blowing :). Thank you in advance!
Bro, There’s no one in the world who can teach quantum mechanics as well as you do. My professor can’t even answer my questions about anything i ask to her; she just gets stuck on her papers or PDFs. Ily
All the videos I watched from the channel, from the mundane topics, such as cheese and olive oil, to the complex topics, such as quantum mechanics, provide accurate, explicit, and most importantly, comprehensible description and explanation. Truly one of the highest quality scientific popularization channels ever made. Well done, sir, and thank you.
RUclips recommended this to me. I saw the intro and was like: "See the previous tutorial? Nonsense! It's just a bit of math, how dense do you think I am?" ... I has been a long time since I last heard so many words, of which I could follow so few, due to my own lack of knowledge. I love it! (And will be back once I've seen the previous installments)
Introduction to behavioural biology was closer to my wheal house 😅😅😅 but if we wouldn't challenge our self's we couldn't learn any of those words and loose the few high-school might have vaguely mentioned once 😉. ruclips.net/p/PLqeYp3nxIYpF7dW7qK8OvLsVomHrnYNjD www.robertsapolskyrocks.com/intro-to-human-behavioral-biology.html#
The way you explain things is absolutely mindblowing! I have been reading a lot but it was your videos that helped me grasp the concepts clearly. THANK YOU SO MUCH Professor!
''quantum mechanics is a probabilistic way of viewing reality that is difficult for our classically trained brains to comprehend but nevertheless this is how the universe operates on this scale.''Amazing line Sir
Thanks for uploading your video. It was an extremely clear exposition. However, I did spot a few small inaccuracies in your video. The wavefunction is related to the vectors of the Hilbert space by ψ(x)= where |x> is a position eigenstate. The vector |ψ> does not vary with position (the information for all x is encoded into the vector, whereas in your explanation the expansion has components which seemed to depend on x, which takes uncountably many values). We can also do quantum mechanics in the momentum representation using ψ(p)= where |ψ> is the same state. Strictly speaking, you made a choice that the normalization constant, a, was real and positive when you normalized your wavefunction. Wavefunctions which differ by a constant phase factor represent the same physical state, so ψ(x) and -ψ(x), for instance, are equally good at representing a quantum state. It is for this reason that your explanation of the double slit experiment is problematic, it is not very natural to add together wavefunctions, since if ψ and φ are two wavefunctions then the wavefunction ψ+φ and ψ-φ do not represent the same physical state. After normalizing and taking the modulus we find that these combinations give entirely different predictions for the probability density for the particle hitting the screen (you slightly misspoke when you included some coefficients in front of the two wavefunctions: you referred to them as probabilities rather than amplitudes). Incidentally, the quick way of working out the expectation of the kinetic energy is to write it is as =|| φ ||²/2m where φ=pψ, this avoids computing a second derivative and is especially labour-saving when working in three dimensions.
@@jacobvandijk6525 The state |a> would be the eigenstate such that (in 1-D) (x^)|a>=a|a>, thus |a> is an eigenstate of the position operator x^ with eigenvalue a. Now there are other position eigenstaes with (x^)|b>=b|b>, for b not equal to a. They are orthogonal =0 (a not equal to b). It is usual to normalize so that is the Dirac delta function of a-b. Then we have the completeness relation: 1=∫|a> is a specific eigenstate, but x is arbitrary, which is why we get a function. All the spatial dependence of the wavefunction is encoded into |ψ>. We extract that information at any position by taking the inner product with
@@jacobvandijk6525 Actually it is the Dirac delta in this case, since the eigenvalues form a continuum: Thus if S=∫|a>=∫|a>da=∫|a>δ(a-b)da=|b> for every |b>, and hence S=1.
Wow your explanations are awesome! I'm looking forward to the next part :) Thanks for the video. I really learned and understood a few things about wave functions.
My quantum mechanics savior🎉🎉🎉 I’m taking calculus 3 and differential equations this semester and together with modern physics. The quantum mechanics part frustrates me due to my math level😅But nothing is too difficult to overcome as long as I put enough energy into it!
I'm going to sit here and nod my head, like I am following you perfectly. Then quietly make my way out the door and ask myself, "Self, you have any idea what he was talking about?" "Oh, yeah. All expect for one part. The part after 'vector space'."
We are excited to host Dave sir on a live show @11.30 AM IST on 15th August. Get ready to ask him anything about physics! Comment your questions on physics .
It is not the wave fuctions that are the vectors in vector space. The coefficients are as part of the linear combinations. The vectors represents the quantum states that are quantities like spin, position or momentum. The wave functions (which act on the states) are the basis for the probability amplitutes.
I've never been one for math, but I'm hoping to absorb a greater understanding of quantum physics through your excellent videos. My question is, if a given solitary electron is literally passing through both slits and is literally in both positions at the same time, then why do we speak of probabilities and expectations? Why do we say its position is probabilistic? If it's 'probably' at this or that position, then it's not in both places, right? Otherwise we'd just list all its positions. It wouldn't be probabilistic, we'd know that its positions are at both slits. The example of the heat map used to find the most likely landing zone of a ball thrown out a window requires multiple throws of the ball and a single landing for each throw, but we're talking about a single electron--in one go--being in all those places at once--and even accepting that's the case, then we know each of its positions, and they're all certain. But they are not considered certain? We're using equations that give us an estimate of its actual position as though it only has one true position, and that the other locations are merely possibilities that arise as a consequence of not knowing the one actual position that it really has. So either it's in both places at once, or it's in only one and we're guessing which is the most likely. Which is it? Please don't say both!
The electron 'in flight' is not a localised projectile or corpuscle. It exists only as a wave - essentially a wave of possibility. As such, we cannot say the electron has a single definite position until it is absorbed by a detector, after which the other probability amplitudes expressed by the wave 'collapse' (because they are no longer possible once the energy, momentum, mass and charge of the electron have been absorbed by something). The wave is what passes through both slits - this is normal behaviour for waves after all - but the electron does not follow a trajectory like a cannonball. The reason why this is difficult to understand is that our usual mental picture of an electron (a tiny speck) is wrong.
Great video! If the wavefunctions are vectors in a Hilbert space what are the basis vectors? if the wavefunction describes a quantum state, lets say an sp3 orbital then does that mean the basis vectors as the individual s and p orbitals? And is that why these can be made up using basis set? Are basis sets and basis vectors the samething?
Sir your explanation is excellent but I have a confusion Sir you told that the presence of an electron is diffused. So I have a question that is the diffusion of presence of electron is due to its wave nature ? I hope that you will clear my doubt. Thank you sir
Surely when you are multiplying d/dx in the derivation of kinetic energy operator it should not be the second derivative but the first derivative squared? Correct me if I am wrong. Great Video as always!.
no that's how it works, notice that the momentum operator occurs twice so you have a derivative acting on a derivative which is necessarily the second derivative
to make sure whether the functions are well behaved I need to make sure it is single valued? Continous and find the integration of the square of the function and see whether there’s a finite value after integrating in provided range? Can you kindly correct me if im wrong Your sincerely
At 20:10, you say that multiplying the two partial derivatives goes as (d/dx)(d/dx) = d^2/dx^2. I'm not gonna pretend that I'm reinventing quantum physics, but shouldn't it be equal to the first derivative squared instead of giving the second derivative? I've looked it up, and I figured that there's a flaw in my reasoning. But why isn't it (d/dx)^2?
that notation acts as an operator, it has to act on something, which would be the function directly to its right. so with the operator acting twice, you get one derivative, and then another, so the second derivative. the first derivative squared would have to be the operator acting on a function and then parentheses around all of that with an exponent outside.
But wait... my book literally says, "In quantum mechanics the average is usually the quantity of interest; in that context it has become to be called the 'expectation value.' It's a misleading term, since it suggests that this is the outcome you would be most likely to get if you made a single measurement (that would be the most probable value, not the average value) - but I'm afraid we're stuck with it." This seems at odds with what you're saying in the video. It seems that you are saying that the expectation value, in fact, is the most probable value, and not the average value. I am confusion.
The expectation value is NOT the most probable value. I had some homework for my quantum mechanics class, where we had to calculate both, expecation value and most probable value and then explain why they can be different. Simple example: imagine any wave function that is symmetric with respect to the y-axis and zero for x=0. The expecation value would be zero, while the most probable values would be the ones where |Ψ(x)|² has it's both maxima (one in the positive and one in the negative region.
hey serious question. Can you explain how water conducts electricity? Or is it the ions in salt water that do the actual conducting and not the water itself? I learned in high school chemistry that water does not conduct electricity and this was demonstrated by trying to send an electric current through water to turn on or light up the light bulb. Water is polar but electrically neutral, and I learned in college physics that if water was positive or negative it would repel itself and cease being water. I understand that charged objects attract with neutral objects. I dont understand how water itself could conduct electricity. Are you trying to say that ions in water, or an aqueous solution, conducts electricity? I would understand that
the wave function is not really a function. it is a section in a complex line bundle over the physical space. to really understand it requires deep knowledge in topology.
@@ProfessorDaveExplains Dear Dave, for example, I recommend this video, ruclips.net/video/V49i_LM8B0E/видео.html at 14:30 professor of mathematical physics Frederic Schuller explains it but the whole course needs to be watched to understand it but his summary about it is in the above video in give time frame.
@@ProfessorDaveExplains the wave function is not a function it is a scalar field on the base space. and a function is not a scalar field. fields are always sections and there are differences , on a function you act a covariant derivative on a trivial manner, on a C- section you can act on a non- trivial manner.
I'm not really sure what any of that means, but psi of x is a function of x so I don't see how that wouldn't be considered a function. But I guess I'll take your word for it.
@@ProfessorDaveExplains If you can do the M x C covariant derivative on a trivial manner then it is a function but the fact is that you cannot always do it unless you use cartesian coordinates. Therefore Psi is not a function. I recommend the course linked above.
@@ProfessorDaveExplains Yess please do a botany series. I'm super interested in it but I really don't know where or how to start learning because I know so little about botany.
You describe the expectation value of an operator as the most likely value. I don’t think this is correct - “most likely” suggests a probabilistic “mode”, rather than a probabilistic “mean” which is what the expectation value corresponds to.
I'm starting prof. Dave syndicate (A team that supports sir's channel to grow by sharing or etc (if we can't support on patron let's support in this way) :) ) let's make a discord channel or insta page to make sir more famous and share knowledge #prof.davesyndicate like this comment if you agree
Thanks for taking the time to cover these higher-level topics. I know they don't perform as well as some of your lower-level videos, but this is incredibly helpful to college-level students such as myself whose professors glossed over most of this information.
This is NOT high level. More like basics ^^
@@boredscientist5756 Boooooo!!
@@Sce.e ?
@@boredscientist5756 which is why they said "higher-level" and not high-level, as in comparing to other videos in the channel. Check your logic and understanding of language before you criticize what people may find challenging or high-level.
@@arnoldschwarz6191 not higher level, just basics.... check the definition of "basic", please.
Professor Dave, I can’t thank you enough for all the effort you put into making this content. I can assure you it‘s been very helpful for students all over the world !
I‘ve recently started a quantum chemistry course at university and came to understand it better after watching your series.
If you are interested, please make a video on experimental application of quantum mechanics (for example, Hartree-Fock approximation) or elaborate on various interpretations of quantum mechanics (I find the many-world interpretation particularly mind -blowing :). Thank you in advance!
You deserve a Nobel Prize in Physics for simplifying it! Thanks!
Kuch bhi 😂😂
No.
Bro, There’s no one in the world who can teach quantum mechanics as well as you do. My professor can’t even answer my questions about anything i ask to her; she just gets stuck on her papers or PDFs. Ily
All the videos I watched from the channel, from the mundane topics, such as cheese and olive oil, to the complex topics, such as quantum mechanics, provide accurate, explicit, and most importantly, comprehensible description and explanation. Truly one of the highest quality scientific popularization channels ever made. Well done, sir, and thank you.
You really do know a lot about science stuff, Professor Dave. There's always a video of yours explaining what I need
RUclips recommended this to me.
I saw the intro and was like: "See the previous tutorial? Nonsense! It's just a bit of math, how dense do you think I am?"
... I has been a long time since I last heard so many words, of which I could follow so few, due to my own lack of knowledge. I love it! (And will be back once I've seen the previous installments)
Introduction to behavioural biology was closer to my wheal house 😅😅😅 but if we wouldn't challenge our self's we couldn't learn any of those words and loose the few high-school might have vaguely mentioned once 😉.
ruclips.net/p/PLqeYp3nxIYpF7dW7qK8OvLsVomHrnYNjD
www.robertsapolskyrocks.com/intro-to-human-behavioral-biology.html#
If you work hard at it, you'll eventually start to get it. Dave's videos are a superb, succinct summary of the subject.
This helps me not only get more familiar with quantum stuff, but also integrate what I learned in wavelet transformation. Much thanks to Prof Dave.
He know a lot about science stuff professor Dave explains!!!
Thank you! I am a 16 year old student getting into physics, your videos are extremely helpful :)
You made my studying for Final Bachelor's exam much easier and more entertaining.. Thank you very much!
The way you explain things is absolutely mindblowing! I have been reading a lot but it was your videos that helped me grasp the concepts clearly. THANK YOU SO MUCH Professor!
Professor Dave is one of my favourite channels on RUclips.Keep going. This channel deserves more like and subscribers..Superb Explanation..
i didnt get this at all until 23 minutes ago, you are terrific. I have been struggling with this formy quantum module, thank you sooo much
By far the most clear explanation about this subject!
''quantum mechanics is a probabilistic way of viewing reality that is difficult for our classically trained brains to comprehend but nevertheless this is how the universe operates on this scale.''Amazing line Sir
Thanks!
Thanks for uploading your video. It was an extremely clear exposition. However, I did spot a few small inaccuracies in your video.
The wavefunction is related to the vectors of the Hilbert space by ψ(x)= where |x> is a position eigenstate. The vector |ψ> does not vary with position (the information for all x is encoded into the vector, whereas in your explanation the expansion has components which seemed to depend on x, which takes uncountably many values). We can also do quantum mechanics in the momentum representation using ψ(p)= where |ψ> is the same state.
Strictly speaking, you made a choice that the normalization constant, a, was real and positive when you normalized your wavefunction. Wavefunctions which differ by a constant phase factor represent the same physical state, so ψ(x) and -ψ(x), for instance, are equally good at representing a quantum state. It is for this reason that your explanation of the double slit experiment is problematic, it is not very natural to add together wavefunctions, since if ψ and φ are two wavefunctions then the wavefunction ψ+φ and ψ-φ do not represent the same physical state. After normalizing and taking the modulus we find that these combinations give entirely different predictions for the probability density for the particle hitting the screen (you slightly misspoke when you included some coefficients in front of the two wavefunctions: you referred to them as probabilities rather than amplitudes).
Incidentally, the quick way of working out the expectation of the kinetic energy is to write it is as =|| φ ||²/2m where φ=pψ, this avoids computing a second derivative and is especially labour-saving when working in three dimensions.
@@jacobvandijk6525 The state |a> would be the eigenstate such that (in 1-D) (x^)|a>=a|a>, thus |a> is an eigenstate of the position operator x^ with eigenvalue a. Now there are other position eigenstaes with (x^)|b>=b|b>, for b not equal to a. They are orthogonal =0 (a not equal to b). It is usual to normalize so that is the Dirac delta function of a-b. Then we have the completeness relation: 1=∫|a> is a specific eigenstate, but x is arbitrary, which is why we get a function. All the spatial dependence of the wavefunction is encoded into |ψ>. We extract that information at any position by taking the inner product with
@@jacobvandijk6525 Actually it is the Dirac delta in this case, since the eigenvalues form a continuum: Thus if S=∫|a>=∫|a>da=∫|a>δ(a-b)da=|b> for every |b>, and hence S=1.
Dave is a god, making us smarter everyday.
Are you stupid 😡
Delete it
@@hal5530 what r u on
@@hal5530 no u
HAL damn why u mad
Have an exam on Quantum Physics in a day and one on Atomic Physics the next day. This is a God save, thank you Dave.
The last 6 videos of this series are beautifully mind bending
the only teacher that can make me understand quantum particles
Sir ur doing a fentabulous job by posting the very useful and easily understandable videos of all subjects everyday. Hats off ur awesome.
Great explanation of the topic! Simple, smooth, inclusive and a lot better than most textbooks. Thanks...
Wow your explanations are awesome! I'm looking forward to the next part :)
Thanks for the video. I really learned and understood a few things about wave functions.
you are doing a great job. The content of this series is quite good, especially for someone who wants to dive into the matter
Best explanation of this topic ever ! Thank you eternally! 🙏🏻
My quantum mechanics savior🎉🎉🎉 I’m taking calculus 3 and differential equations this semester and together with modern physics. The quantum mechanics part frustrates me due to my math level😅But nothing is too difficult to overcome as long as I put enough energy into it!
You've explained it very well and it would be much harder for me to survive my courses if it wasn't for you. Thanks!
I didn't really get Hilbert space before, but you explained it quite well. I like the pacing of the video.
thanks for making us smarter every day
someone : how can a student learn all subject,if a teacher teacher teaches only one subject
me : i know a teacher who can teach all subjects
I'm going to sit here and nod my head, like I am following you perfectly. Then quietly make my way out the door and ask myself, "Self, you have any idea what he was talking about?" "Oh, yeah. All expect for one part. The part after 'vector space'."
You are literally a bless that god has sent to amaze us every single day by your intelligence. Keep it up dear.
Knowledge *
Very good explanation! Thanks Prof.
THANK YOU SOOOOOOOOOOO MUCH for this info your the best
Can’t wait for more of this quantum physics stuff
We are excited to host Dave sir on a live show @11.30 AM IST on 15th August. Get ready to ask him anything about physics!
Comment your questions on physics .
Awaiting for the session
This series is excellent.
Excellent video for learners of quantum mechanics.
It is not the wave fuctions that are the vectors in vector space. The coefficients are as part of the linear combinations. The vectors represents the quantum states that are quantities like spin, position or momentum. The wave functions (which act on the states) are the basis for the probability amplitutes.
I've never been one for math, but I'm hoping to absorb a greater understanding of quantum physics through your excellent videos. My question is, if a given solitary electron is literally passing through both slits and is literally in both positions at the same time, then why do we speak of probabilities and expectations? Why do we say its position is probabilistic? If it's 'probably' at this or that position, then it's not in both places, right? Otherwise we'd just list all its positions. It wouldn't be probabilistic, we'd know that its positions are at both slits.
The example of the heat map used to find the most likely landing zone of a ball thrown out a window requires multiple throws of the ball and a single landing for each throw, but we're talking about a single electron--in one go--being in all those places at once--and even accepting that's the case, then we know each of its positions, and they're all certain. But they are not considered certain? We're using equations that give us an estimate of its actual position as though it only has one true position, and that the other locations are merely possibilities that arise as a consequence of not knowing the one actual position that it really has. So either it's in both places at once, or it's in only one and we're guessing which is the most likely. Which is it?
Please don't say both!
The electron 'in flight' is not a localised projectile or corpuscle. It exists only as a wave - essentially a wave of possibility. As such, we cannot say the electron has a single definite position until it is absorbed by a detector, after which the other probability amplitudes expressed by the wave 'collapse' (because they are no longer possible once the energy, momentum, mass and charge of the electron have been absorbed by something). The wave is what passes through both slits - this is normal behaviour for waves after all - but the electron does not follow a trajectory like a cannonball. The reason why this is difficult to understand is that our usual mental picture of an electron (a tiny speck) is wrong.
Actually this helps a lot...So beneficial....Thank you very much prof...❤️❤️
This is very informative vedio thank you sir
Wow nice work
love you prof Dave
Thanks professor Dave for considering my e-mail...I knew you would
Great video! If the wavefunctions are vectors in a Hilbert space what are the basis vectors? if the wavefunction describes a quantum state, lets say an sp3 orbital then does that mean the basis vectors as the individual s and p orbitals? And is that why these can be made up using basis set? Are basis sets and basis vectors the samething?
Thank you very much
Came for the flat earthers, stayed for the quantum mechanics
A wonderful tutorial !!!
great content
Excellent! Thanks
Awesome video
beginning of the playlist: fun facts and helpful advice on how to understand concepts in the subject
end of the playlist: *all I see is suffering*
Sir your explanation is excellent but I have a confusion
Sir you told that the presence of an electron is diffused. So I have a question that is the diffusion of presence of electron is due to its wave nature ? I hope that you will clear my doubt.
Thank you sir
For the double split experiment; what is the reasoning behind multiplying the probability (a1) and wavefunction (psi 1) for the individual slit.
Professor could you explain for us more about relativity?! Thank you so much
Hey Dave, can you do a series on linguistics?
one day!
Surely when you are multiplying d/dx in the derivation of kinetic energy operator it should not be the second derivative but the first derivative squared? Correct me if I am wrong. Great Video as always!.
no that's how it works, notice that the momentum operator occurs twice so you have a derivative acting on a derivative which is necessarily the second derivative
@@ProfessorDaveExplains ahh understood its operator not a substitution got it :)
Thanks
Love your voice.
to make sure whether the functions are well behaved
I need to make sure it is single valued?
Continous and find the integration of the square of the function and see whether there’s a finite value after integrating in provided range?
Can you kindly correct me if im wrong
Your sincerely
i love the you explain.
Dave have you done a video about Fourier transforms/ series? And if so where would I find it?
Please make a video on what exactly Google has solved using quantum computers with respect to the eigen solver.
At 20:10, you say that multiplying the two partial derivatives goes as (d/dx)(d/dx) = d^2/dx^2. I'm not gonna pretend that I'm reinventing quantum physics, but shouldn't it be equal to the first derivative squared instead of giving the second derivative? I've looked it up, and I figured that there's a flaw in my reasoning. But why isn't it (d/dx)^2?
that notation acts as an operator, it has to act on something, which would be the function directly to its right. so with the operator acting twice, you get one derivative, and then another, so the second derivative. the first derivative squared would have to be the operator acting on a function and then parentheses around all of that with an exponent outside.
Can we say that expectation value are sumation of eigen values times probblity of each vakue ?
Holy fucking shit this just made so much sense out of what ever the hell my textbook is trying to teach me!!!!!
Superb
Thanks!!!!
Yeah Professor Dave! Yeah psience!
P-Chem PTSD flashbacks intensify
But wait... my book literally says, "In quantum mechanics the average is usually the quantity of interest; in that context it has become to be called the 'expectation value.' It's a misleading term, since it suggests that this is the outcome you would be most likely to get if you made a single measurement (that would be the most probable value, not the average value) - but I'm afraid we're stuck with it." This seems at odds with what you're saying in the video. It seems that you are saying that the expectation value, in fact, is the most probable value, and not the average value. I am confusion.
The expectation value is NOT the most probable value. I had some homework for my quantum mechanics class, where we had to calculate both, expecation value and most probable value and then explain why they can be different. Simple example: imagine any wave function that is symmetric with respect to the y-axis and zero for x=0. The expecation value would be zero, while the most probable values would be the ones where |Ψ(x)|² has it's both maxima (one in the positive and one in the negative region.
hey serious question. Can you explain how water conducts electricity? Or is it the ions in salt water that do the actual conducting and not the water itself? I learned in high school chemistry that water does not conduct electricity and this was demonstrated by trying to send an electric current through water to turn on or light up the light bulb. Water is polar but electrically neutral, and I learned in college physics that if water was positive or negative it would repel itself and cease being water. I understand that charged objects attract with neutral objects. I dont understand how water itself could conduct electricity. Are you trying to say that ions in water, or an aqueous solution, conducts electricity? I would understand that
Yes, ocean water conducts electricity because of the ions, absolutely pure water will not.
@@ProfessorDaveExplains ok. Thank you. I was confused.
the wave function is not really a function. it is a section in a complex line bundle over the physical space. to really understand it requires deep knowledge in topology.
The wavefunction is a function. This video is about the wavefunction.
@@ProfessorDaveExplains Dear Dave, for example, I recommend this video, ruclips.net/video/V49i_LM8B0E/видео.html at 14:30 professor of mathematical physics Frederic Schuller explains it but the whole course needs to be watched to understand it but his summary about it is in the above video in give time frame.
@@ProfessorDaveExplains the wave function is not a function it is a scalar field on the base space. and a function is not a scalar field. fields are always sections and there are differences , on a function you act a covariant derivative on a trivial manner, on a C- section you can act on a non- trivial manner.
I'm not really sure what any of that means, but psi of x is a function of x so I don't see how that wouldn't be considered a function. But I guess I'll take your word for it.
@@ProfessorDaveExplains If you can do the M x C covariant derivative on a trivial manner then it is a function but the fact is that you cannot always do it unless you use cartesian coordinates. Therefore Psi is not a function. I recommend the course linked above.
Basically, everybody can skip the first chapter in Griffiths by just watching this, which is a CONSIDERABLY better explanation.
Hi sir big fan give me one reply
yo!
@@ProfessorDaveExplains thank you sir I am you member for your channel please post something in community post for members of your channel
i'll do an early preview soon, maybe for my new botany series
@@ProfessorDaveExplains nice
@@ProfessorDaveExplains Yess please do a botany series. I'm super interested in it but I really don't know where or how to start learning because I know so little about botany.
To the point
Concise
Can a star be massive enough to fuse iron?
Of course, most stars do.
are you teaching the phd holders here?
No, this would be latter half of undergrad. But it's not simple so don't feel bad if it's confusing!
2:48 Dave becoming a pirate: "are are" (in the title)
legend. I live in Mount Olympus.
I didn't understand the double are. What going on?
You describe the expectation value of an operator as the most likely value. I don’t think this is correct - “most likely” suggests a probabilistic “mode”, rather than a probabilistic “mean” which is what the expectation value corresponds to.
You are my jesus !
I'm starting prof. Dave syndicate (A team that supports sir's channel to grow by sharing or etc (if we can't support on patron let's support in this way) :) ) let's make a discord channel or insta page to make sir more famous and share knowledge
#prof.davesyndicate like this comment if you agree
the dislikes are flat earthers
And also binod
👏
Diosito por favor guíame
NOT sleep Not job Not Talk
Now, if only I had this for my QM class...
People that watch this in summer are complete nerds😂 yes I came here to comment that🤣
HOW MANY VIEWS?!?! 127K *sticker flutes*
How am I so early OwO
... (sad confused noises) ...
Professor Dave do be kinda cute tho
Shure I iz up to speed. You have sum? But mind, that other professar always makez me le good prices for ze spee.