00:03 Wave packet describes particle motion in quantum mechanics 02:41 Wave packet represents particle's motion and its evolution through space. 07:58 Different frequencies travel at the same or different speeds based on the medium's dispersion. 10:18 Wave packet can be simplified using Taylor series expansion 15:44 The wave packet comprises a plane wave solution and a modulating function. 18:10 Comparing the speeds of plane wave and modulating function. 22:55 Group velocity represents the velocity of the entire wave packet. 25:04 Group velocity and phase velocity can be equal, unequal, or opposite. 29:48 Group velocity is related to particle energy and momentum. 32:08 In quantum mechanics, the group velocity represents the particle's velocity. 36:54 Group velocity is the same as the particle's velocity, but phase velocity may not have a physical significance. 38:53 Phase velocity is always greater than the speed of light 43:11 Wave packet idea discussed, more details next class
Honestly, this is the best Video explaining the concept in-depth. Like, concepts of Quantum Mechanics require an in-depth explanation backed with Mathematical proves(although beyond scope) so as to justify presence of every term and it's use. Thanks a lot sir-loved the lecture-was 10000× better than my clg lecture which was, actually, equivalent to 1% of this video
First of all, I love this video!! I am a second year grad student in physics at Tel Aviv University, and I have never heard this explained that well. Second, why is the modulating function only a function of x? Shouldn’t it be a function of x & t?
The thing is that so called "wave packet" is a summation of plane waves of varying frequencies and amplitudes, which introduces the analytical tool of integration over continuous range of k (momentum). Although it is now confined spatially (as we make its momentum more uncertain) and wavefunction becomes normalized;... it is not quantized yet. The fact that integration is being used here, we are still dealing with continuous variable of k. This means that we have a vector space with orthonormal base of infinite size of eigenstates. The result of a precise measurement on a single quantum system is always one of the eigenvalues of the measured observable (whaterever operator we apply to quantum system). If we still have infinite amount of eigenstates (eigenvectors).
Lots of confusion between math and physics here. A single quantum has only energy, momentum, angular momentum and charge. These are the physical properties we are measuring with a detector. The so called "wave" does not exist in nature. It's an average quantity that shows up (indirectly) in histograms of many individual quantum measurements. If you want to compare this to dice... one of the outcomes of a dice throw is a number between one and six. That's the "quantum" we are getting from dice. The average of many dice throws is a number close to 3.5... which is clearly not a possible individual outcome.
Thank you so much sir...these videos are very much useful to me ...gives more clarity....please keep give such useful videos about complex topics in physics
Wow! Now I'm almost in Quantum Heaven, where full understanding is achieved! I can't wait to learn the uncertainty principle! Great foundational video! I am finally learning the science instead of the scientists!...
This is also like how Area 7 of the visual cortex works, normally modeled by Gabor filters (a sinusoidal multiplied by a normal curve), but of course meat is approximate. I wonder if the brain's tendency to think of particle-like versus wave-like properties and thus fail to understand QM is a consequence of automatic post-processing of the visual signal after Area 7 to feed to the topographic maps (terrible term) that are used to understand position and velocity to.predict trajectories.
40:40 I used the formula VpVg=C² . During my semester exam of EM Theory. And phase velocity came out to be greater than speed of light and I was confused and rechecked calculation. But still it was greater than c. But I write it anyway and thinking the examiner will laugh at my solution 😂
Dr. Das--Excellent explanatory video!! Thank you so much for uploading this. And so the representation of the wave packet is essentially a Fourier transform?
Sir ...I am in. Class 12 th ...but I seriously like your videos and a have seen your all video of this beautiful series...but sir many people are saying me that this is not your syllabus so can't watch these type of videos...but sir at last I want your comment on this situation... should I watch your videos.... please sir give me answer.....
Yes ...yes sir but sir my question is if I am able to understand your videos so can I watch your videos ... instead of doing chat in insta or something 😂....
By the way sir ...you have a very nice way to teach ous ... seriously I am saying sir .. although I am not using English language to much with my friends or family...but still I am able to understand you in your videos this shows that you have a great way to understand topic to student and experience also ....I not kidding sir 😂 but seriously I can say ....that time is not so far from you when when India will say you Indian feymen ❤...thanku a lot sir for your beautiful videos ......love you ❤❤❤❤❤
@@Aashu3103 Once you have completed your 12th grade studies for the day, take some time to view these lectures. Even though they are not part of the syllabus, if you find them interesting and comprehend them, there is no reason why you shouldn't watch them.
Could you please clarify why the modulating function typically depends only on x, rather than on both x and t? If the modulation is time-dependent,, shouldn't the function involve both x and t?And thank you so much for the amazing lectures!!
I uploaded this video yday, but immediately realised that there was an editing mistake. So had to delete that video and reupload it today with the necessary correction
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00:03 Wave packet describes particle motion in quantum mechanics
02:41 Wave packet represents particle's motion and its evolution through space.
07:58 Different frequencies travel at the same or different speeds based on the medium's dispersion.
10:18 Wave packet can be simplified using Taylor series expansion
15:44 The wave packet comprises a plane wave solution and a modulating function.
18:10 Comparing the speeds of plane wave and modulating function.
22:55 Group velocity represents the velocity of the entire wave packet.
25:04 Group velocity and phase velocity can be equal, unequal, or opposite.
29:48 Group velocity is related to particle energy and momentum.
32:08 In quantum mechanics, the group velocity represents the particle's velocity.
36:54 Group velocity is the same as the particle's velocity, but phase velocity may not have a physical significance.
38:53 Phase velocity is always greater than the speed of light
43:11 Wave packet idea discussed, more details next class
Thank you! From someone who also loves physics!
Your video has been helpful in my quantum mechanics classes.
Much love from Nigeria, Africa.
Thank you very much sir. You are helping a lot of poor students who cannot afford to learn in expensive universities. Love you sir ❤❤❤
Kindly upload more lectures sir. U r the master piece of teaching profession sir.
Honestly, this is the best Video explaining the concept in-depth. Like, concepts of Quantum Mechanics require an in-depth explanation backed with Mathematical proves(although beyond scope) so as to justify presence of every term and it's use. Thanks a lot sir-loved the lecture-was 10000× better than my clg lecture which was, actually, equivalent to 1% of this video
Sir pls keep going,,, plss don't stop this series
This playlist is a great gift professor ❤
First of all, I love this video!! I am a second year grad student in physics at Tel Aviv University, and I have never heard this explained that well.
Second, why is the modulating function only a function of x? Shouldn’t it be a function of x & t?
It's a function of space and time, but separation of variables can be achieved for time-independent potentials.
As usual a clear and physics marred to math approach...nicely done man!!
A remarkable teaching by a remarkable teacher
Thanks a lot sir
you have really nice communication with the head nodding when talking about definite contexts
U r the best Explainer ❤❤❤❤
Simply the best explanation I ever heard. Brilliant. Thank you.
I love your teaching style sir ❤
34:16 formulas to remember , for relativistic also
Very Helpful, Thank you very much for all the efforts!!
The thing is that so called "wave packet" is a summation of plane waves of varying frequencies and amplitudes, which introduces the analytical tool of integration over continuous range of k (momentum). Although it is now confined spatially (as we make its momentum more uncertain) and wavefunction becomes normalized;... it is not quantized yet. The fact that integration is being used here, we are still dealing with continuous variable of k. This means that we have a vector space with orthonormal base of infinite size of eigenstates. The result of a precise measurement on a single quantum system is always one of the eigenvalues of the measured observable (whaterever operator we apply to quantum system). If we still have infinite amount of eigenstates (eigenvectors).
Lots of confusion between math and physics here. A single quantum has only energy, momentum, angular momentum and charge. These are the physical properties we are measuring with a detector. The so called "wave" does not exist in nature. It's an average quantity that shows up (indirectly) in histograms of many individual quantum measurements. If you want to compare this to dice... one of the outcomes of a dice throw is a number between one and six. That's the "quantum" we are getting from dice. The average of many dice throws is a number close to 3.5... which is clearly not a possible individual outcome.
Thank you so much sir...these videos are very much useful to me ...gives more clarity....please keep give such useful videos about complex topics in physics
Wow! Now I'm almost in Quantum Heaven, where full understanding is achieved! I can't wait to learn the uncertainty principle! Great foundational video! I am finally learning the science instead of the scientists!...
What a great teacher
Love you sir...❤ please keep these videos coming❤❤❤
This is also like how Area 7 of the visual cortex works, normally modeled by Gabor filters (a sinusoidal multiplied by a normal curve), but of course meat is approximate. I wonder if the brain's tendency to think of particle-like versus wave-like properties and thus fail to understand QM is a consequence of automatic post-processing of the visual signal after Area 7 to feed to the topographic maps (terrible term) that are used to understand position and velocity to.predict trajectories.
Thank you, very clear explanation! 😊
40:40 I used the formula VpVg=C² . During my semester exam of EM Theory. And phase velocity came out to be greater than speed of light and I was confused and rechecked calculation. But still it was greater than c. But I write it anyway and thinking the examiner will laugh at my solution 😂
Dr. Das--Excellent explanatory video!! Thank you so much for uploading this. And so the representation of the wave packet is essentially a Fourier transform?
Sir ...I am in. Class 12 th ...but I seriously like your videos and a have seen your all video of this beautiful series...but sir many people are saying me that this is not your syllabus so can't watch these type of videos...but sir at last I want your comment on this situation... should I watch your videos.... please sir give me answer.....
For 12th, many topics will be out of syllabus.
Yes ...yes sir but sir my question is if I am able to understand your videos so can I watch your videos ... instead of doing chat in insta or something 😂....
By the way sir ...you have a very nice way to teach ous ... seriously I am saying sir .. although I am not using English language to much with my friends or family...but still I am able to understand you in your videos this shows that you have a great way to understand topic to student and experience also ....I not kidding sir 😂 but seriously I can say ....that time is not so far from you when when India will say you Indian feymen ❤...thanku a lot sir for your beautiful videos ......love you ❤❤❤❤❤
@@Aashu3103true , Good to see someone is learning for the sake of Interest ✨💫
@@Aashu3103 Once you have completed your 12th grade studies for the day, take some time to view these lectures. Even though they are not part of the syllabus, if you find them interesting and comprehend them, there is no reason why you shouldn't watch them.
Could you please clarify why the modulating function typically depends only on x, rather than on both x and t? If the modulation is time-dependent,, shouldn't the function involve both x and t?And thank you so much for the amazing lectures!!
26:30 pv anf gv
Sir, please discuss about wave properties like interference,diffraction, polarization etc
plz tell plane wave solution of Schrodinger eq is probably amplitude or wave packet is probably amplitude?
Sir Plz upload atleast 2 lectures a week for the love of students
Another great video
v v v v good lecturer. plz upload soon next video
Please upload Infinite Square well and Finite Potential
Thankyou sir❤
sir can u make series of ct scan machine physics and also as of mri
Awesome!
Can you post your bibliography? It will be so helpful
ty for video, keep going :D
One question at 17.55 will that be f(x) or f(x,t)? Very nice video. Thank you
So sir does plane waves are continuously super positioning as result we see wave packet or they were once superposition and then wave packet is formed
Plz explain
Useful for me
thanks sir
phase velocity is not just an abstract mathematical construction, but we do not have the technology to measure it.
Of course we do.
@@schmetterling4477 the phase velocity is a physical quantity and not just an abstract construct.
please make a scilab tutorial on this.
Is it different than what we have for sound wave ?
With regards to group and phase velocity? No, not really. With regards to what the wave means? Absolutely.
it is Good
Want to learn how the concept of Wave packet leads to the Uncertainty Relations? ruclips.net/video/X4i2asvhPeY/видео.html
Nice!
W 🔥🔥🔥🔥
I am seeing this after my quantum paper exam has ended.. thanks
Write a book, sir!
❤
Is this reupload?
I uploaded this video yday, but immediately realised that there was an editing mistake. So had to delete that video and reupload it today with the necessary correction
@@FortheLoveofPhysicsthanks sir
💕💕
Please sir ...😢give answer 😢
You are absolutely superb but unfortunately, your video uploading frequency is dissatisfying given our excitement to see your videos
Sir everything is good but please write k properly it is really confusing to differentiate between k and R
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