What is a Wave Packet in Quantum Mechanics?
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- Опубликовано: 5 авг 2024
- In Quantum Mechanics, a particle is best described by the concept of a Wave packet. Now, what is a Wave packet? That is what we will discuss in this video.
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In QM, a wave packet is a fundamental concept used to describe the behavior of particles at the quantum level. It represents a localized and often temporary concentration of a particle's probability amplitude in a specific region of space.
Imagine a particle, such as an electron, whose behavior is described by a wave function. This wave function is a mathematical expression that characterizes the probability distribution of finding the particle at various positions in space. A wave packet is essentially a wave function that is strongly peaked in a limited spatial region. Wave packets are crucial for understanding the behavior of particles at the quantum level.
00:00 Introduction
02:21 Wave Particle Duality
06:02 Wave packet
15:44 Plane Waves
20:50 Schrodinger's Equation for Free Particle
27:17 Final Expression of Wave packet
34:21 Physical Interpretation of Wave packet
Source of Simulation of Wavepacket: d-arora.github.io/Doing-Physi...
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We shouldn't complain about waiting for these videos. We should just be thankful for having them! Thank you Dibyajyoti Das!! ❤
A beautifully done video on an important topic. Thank you!
Please continue this series, sir.
Your lectures are absolutely brilliant! Your channel is where I turn to whenever I need deep intuition in physics concepts. I love you.
Really excited I’ve found someone with in depth explanations like yours. Thank you so much!
I don´t have words for describe this video...Thank you so much!!
Sir, please accept my good wishes & gratitude on the occasion of Teachers Day. You are a phenomenal Teacher having immens depth of knowledge. I pray for your good health & prosperity.
Thank you. Best wishes:)
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Aapke jesa koy nahi sir ...aapki video dekha kar mere MSc kafi marks improve huve Hain...🔥
Happy teacher's day sir your lectures help us alot, the way you clear our concepts we are grateful for that
Very informative & Clear explanation..Thank you ...More such videos from ur end sir
Sir,
Best video. It is a must for any one want to understand what is a wave pocket.
They way you approached the need of wave pocket to describe Quantum behaviour. Concluded the video by showing how this wave pocket idea addresses the each bit of QM's mathematical necessity is simply awesome. I couldn't see such a complete explanation so far.
You rock. ❤
Thank you so much sir for explaining the concepts in such a systematic and conceptual form. God bless you each day to come and give you more wisdom and blessings as you teach many students!
Awesome explanation. ¡Thanks!
An excellent teacher.
great work towards 3d schrodinger's wave equation
Brilliant. Thank you.
WOW!! thank you!
I'm a 1st year student of faculty of science in sri lanka..........Thank u so much for this video.
Excellent teaching
great explanation
HAppy Teachers day sir. Kindly upload more lectures.
Thanks a lot sir
you are very fantastic, thank you very much
Sir you are uploading the videos of this series very late
Please try to give 2 or 3 videos in a month atleast 🥺🙏
I will try my best. yes, I am from Assam
Thank you sir.....
Thank you sir 😊
When we see/observe and when we apply measurement method/technique to a quantum system... there is a difference between these two verbs. When we measure it we transform the quantum state |psi> into something that can be approximated with a dirac delta function due to uncertainty principle. What do you mean "when we see a particle it behaves like a particle"?
33:40 there is nuance to saying the wave packet spreads b/c of momentum uncertainty. In wave packets of light, the HUP applies but the wave packet does not spread, as all modes propagate at c = p/E = dp/dE. which is dispersionless.
For a massive particles, there is dispersion because at zero momentum, there is finite energy: mc^2, or minimum cut-off frequency below which no modes exist.
Sir please continue series..
What about Bohmian mechanics, which is the only interpretation of QM that makes some logical sense?
that is the nicest handwriting I have ever seen on a chalkboard
Happy Teachers Day. thanks for this video, I have been eagerly waiting. I hope you will kindly compensate for the long absence by posting videos more frequently😀😀. Really a big fan of your content, and dependent on them.
Thank you :) I will try my best and upload multiple videos in coming weeks.
What bullshit teachers day ?
The horrible management and horrible and terrible disasters of teachers day ........
Only some select unmolested and guys praying for rain are enjoying teachers day
who are the teachers ??? those who are protected by strong political support of the government ...without any sexual harassment.
However political parties for enjoying a piece of farmers land are depriving scholarships ........by imposing exams like NEET where only the politically influenced beggars will get shortlisted in their .......
Always air pollution and seismic sources are finding fault with water
They have overhead projectors only for .......their candidates .......
indirectly influenced by sexual assaults and guys want their beds from Himalayas down to .....cape town
always blaming and accusing ...................where is that packet ???
Rahul .......Robot ...
I love the way you teach sir love you sir from Pakistan
12:08 is not a simple plane wave solution, it's two plane wave solutions with p and -p added together. For new students to understand it, they really need to think of it as a complex wave, with the derivative of the complex part, or the phase = kx - wt, doing the heavy lifting.
The wave packet itself doesn't have nodes in it, it just has a corkscrew real/imaging structure.
Ofc your math is totally correct, but I have seen a lot of confusion develop because they only see pictures of Re(psi), and forget about Im(psi). --ok 32:30 well done.
Would it be correct to regard the energy quantum as Planck used it in his radiation law (h x f) as a wave packet?
Thank you very informative. How did you create the graphs at time stamp at 33.
suppose i solve one dimension box problm using Schrodinger eq. then i will obtain one solution which is also member of a wavepacket ' then how i will form a wavepacket from this single solution. or for 1D box how i can obtain a wavepacket for given conditions for an electron.
iam waiting for next video sir please make it as early as possible sir
Sir please make a couple of videos regarding general relativity. Please sir
Please make videos fastly humble request to you sir😢 these are very helpful ❤❤❤
He is kaafir, don't believe in him bro😢😢,it's all fake .Only read quran👆,
,You will find everything & every question of the universe. Insallah
i was wondering if you are doing any 1 on 1 lessons international?
Happy Teachers Day Sir
Thank you :)
No quiet sure why the integral is being used here if the wave packet is being discribed by a summation of waves w/ discrete k values (quantum number). Don't we want to use Fourier series in this case, not Fourier transform?
Please make a video Bohmian quantum mechanics.
Sir plz upload at least 2 lectures a week, it is doable.
Waiting for ur next video
Theoretical physics is a great course for PHYSICS students from St. Finian's College Secondary School Mullingar Co Westmeath Ireland
Sir mare NET ka subscription lena Hain... abhi ke time... so you're providing recording lecture in this time..& what's the process..?
sir, please create a video on how to simulate a wave packet in scilab.
Are you from Assam originally?
Thanks sir happy teacher's day
Thank you :)
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Still using chalk and board in 2023
Sir Can you please increase your frequency of videos as I have my entrance in December and I want to complete my QM before that.
I will try my best
@@FortheLoveofPhysics Thanks sir, it will be great help to me.
What is grantee that all infinite waves will do constructive interference at that point where particle is present bcz in real case it depends on path difference. now for these waves what is condition for this
It is a general technique. The final nature of the multiplicative modulating function that arises out of it will determine the nature of the wave packet
Thank u
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is solution of Schrodinger eq. represent a wave packet r not?
The solution of SE is one plane wave solution. The wave packet is the linear superposition of many such plane waves.
Thank u
How we can obtain all plane wave solutions by solving Schrodinger eq .present in a wavepacket. For this what procedure we will follow.
Sir, have some questions, where to ask?
Telegram channel. Link in channel about page
@@FortheLoveofPhysics thank you sir
Is there a physical width to the wave packet? What is the order of magnitude. Or is it infinitesimally small, the width?
The width is associated with the uncertainty in measurement of the particle's position
@@FortheLoveofPhysics thanks!
understood that wavepacket is an attempt to somehow combine the particle and it's associated matter wave nature into a single 'thing', it was exaplained wonderfully, but what I am not able to understand is that now how can a wavepacket perform collision with another wavepacket, or how can a wavepacket go under interference as it does not consist of wavefronts, the nature of it being a mathematical concept and our inablility to know the real physical truth because of our incapable measuring devices, is posing this problem in my understanding, if someone know the solution to my doubt or can guide me for this doubt, a reply will be really appreciated..
I'll try: In the double slit experiment i.e. when both slits are open, the electrons (or other particles) hitting the screen form an interference pattern, and that would not be possible if the electrons behaved like little balls. Even if we fire only one electron at a time, so that only one electron at a time is between the double slits and the screens, interference occurs. So we can see that the particles must have wavelike behaviour.
A wave was never observed (or measured), but we see the interference pattern, so that we must assume the particles somehow behave like waves.
But when we measure, we always find only particles, that's "little balls" with a definite location (where they hit the screen i.e.).
But how can the interference patterns form even when only one electron at a time goes through the double slits? The only possible "explanation" ist that the particle goes throught both slits at once and than interferes with itself. As long as it's not measured, it has no definite position, but is in all locations (allowed by the wave packet) at once; it is in superposition. That sounds or is weird, but so is QM!
So the wave packet represents all possible or probable positions of a particle (with higher probabilities at the peaks), that's where there's most likelihood to find the electron when measured.
Only when we measure its position (when it hits the screen i.e.), the superposition of all probable positions "collapeses" into a definite position.
It's not "our incapable measuring devices", but the particles wavelike behaviour (like going through two slits at once or interferring with itself) that doesn't allow us to assign the particle a definite position. Only when measured it randomly assumes a definite position out of the probable ones.
So I think we can say: we never measure a wave (and the wavefunction contains imaginary parts), so it's a mathematical tool, but it has its "representation" in reality, the interference patterns i.e.
Hope this helps?
@Gwunderi25 hmmm, I get it more, I have one question in mind that we have prepared a mathematical explanation that is well describing the behavior of electron, but, like in collision of 2 tennis balls I can see how they interact with each other and follow their resultant trajectory and hit a wall or something, I want to find out how the electrons actually are interacting with each other so that they give the pattern they give, like in water waves I can see waves colliding and resulting onto bigger waves or collapsing each other, the same way, I want to know what actually the electron is doing in that black box, we have made a explanation and that's fantastic, but my brain further says that "okay, but what are they 'actually ' doing with each other " , maybe because since my childhood, I have been able to see why things are the way they are for example the collision of balls or water waves..I desire to know this too..
@@keshavjindal3294 "How the electrons actually are interacting with each other so that they give the pattern they give …"
The interference pattern appears even if only one electron at a time is fired through the double slits. So we can't say that the electrons interact with each other to form the pattern.
A single electron hits the screen at a random place, but with higher probability at the wave's peaks, and almost zero probability when the wave's amplitude is zero.
The interference pattern is given after a great number of electrons hit the screen, most electrons at the places where the wave has its peaks and almost no electrons at amplitude zero.
So it's the probabilty distribution given by the wave's amplitudes that "creates"*** the interference pattern, and not the electrons interacting with each other.
Sounds weird, I know, not our everyday experience …
***Edit: Better: We SEE an interference pattern on the screen, and find that it corresponds to the interference pattern of a wave going through both slits and than interfering; so we can create a wave function that shows where the electrons are more or less likely to hit the screen.
Happy Teacher's day 😊
Thank you so much 😀
The properties can be measured, but we do not have the instrumentation to do so.
Send all your lectures.
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Don't all waves do that? You have two rotating axes and they just make a shape like that. It's not even that shape though. It's elongated with respect to time. You could probably find planets with cycles that look like that if you put it in the right perspective.
helal la delioğlan
Where does the notion of "particle as localized object" comes from? If my Latin is correct, "particle" only means "little part" and says nothing about its shape, form or nature, just that it is constituent of something bigger. What you say may be best described as "corpuscles" (little bodies), which is a term that was used in the 19th centuries debates about the nature of light, sometimes described as "corpuscular".
In any case where do we observe the "particle" (corpuscle) nature of light or anything else? Not in the photoelectric effect, which only shows that electrons absorb discrete fractions of the light wave (frequency and not amplitude) but not that light is actually made of little objects at all.
I am under the impression that Physics may have fallen into Newtonian legacy pitfalls for no good reason at all.
Also light does not have mass.
I agree that all we observe is quantized transfers between the EM field and (in most cases) the electrons in atoms. We don’t see light “particles” anywhere.
String Theory was not a waste of time. Geometry is the key to Math and Physics.
What if we describe subatomic particles as spatial curvature, instead of trying to describe General Relativity as being mediated by particles?
Quantum Entangled Twisted Tubules: "A theory that you can't explain to a bartender is probably no damn good." Ernest Rutherford
The following is meant to be a generalized framework for an extension of Kaluza-Klein Theory. Does it agree with the “Twistor Theory” of Roger Penrose? During the early history of mankind, the twisting of fibers was used to produce thread, and this thread was used to produce fabrics. The twist of the thread is locked up within these fabrics. Is matter made up of twisted 3D-4D structures which store spatial curvature that we describe as “particles"? Are the twist cycles the "quanta" of Quantum Mechanics?
When we draw a sine wave on a blackboard, we are representing spatial curvature. Does a photon transfer spatial curvature from one location to another? Wrap a piece of wire around a pencil and it can produce a 3D coil of wire, much like a spring. When viewed from the side it can look like a two-dimensional sine wave. You could coil the wire with either a right-hand twist, or with a left-hand twist. Could Planck's Constant be proportional to the twist cycles. A photon with a higher frequency has more energy. ( E=hf, More spatial curvature as the frequency increases = more Energy ). What if gluons are actually made up of these twisted tubes which become entangled with other tubes to produce quarks. (In the same way twisted electrical extension cords can become entangled.) Therefore, the gluons are a part of the quarks. Quarks cannot exist without gluons, and vice-versa. Mesons are made up of two entangled tubes (Quarks/Gluons), while protons and neutrons would be made up of three entangled tubes. (Quarks/Gluons) The "Color Force" would be related to the XYZ coordinates (orientation) of entanglement. "Asymptotic Freedom", and "flux tubes" are logically based on this concept. The Dirac “belt trick” also reveals the concept of twist in the ½ spin of subatomic particles. If each twist cycle is proportional to h, we have identified the source of Quantum Mechanics as a consequence twist cycle geometry.
Modern physicists say the Strong Force is mediated by a constant exchange of Mesons. The diagrams produced by some modern physicists actually represent the Strong Force like a spring connecting the two quarks. Asymptotic Freedom acts like real springs. Their drawing is actually more correct than their theory and matches perfectly to what I am saying in this model. You cannot separate the Gluons from the Quarks because they are a part of the same thing. The Quarks are the places where the Gluons are entangled with each other.
Neutrinos would be made up of a twisted torus (like a twisted donut) within this model. The twist in the torus can either be Right-Hand or Left-Hand. Some twisted donuts can be larger than others, which can produce three different types of neutrinos. Gravity is a result of a very small curvature imbalance within atoms. (This is why the force of gravity is so small.) Instead of attempting to explain matter as "particles", this concept attempts to explain matter more in the manner of our current understanding of the space-time curvature of gravity. If an electron has qualities of both a particle and a wave, it cannot be either one. It must be something else. Therefore, a "particle" is actually a structure which stores spatial curvature. Can an electron-positron pair (which are made up of opposite directions of twist) annihilate each other by unwinding into each other producing Gamma Ray photons?
Does an electron travel through space like a threaded nut traveling down a threaded rod, with each twist cycle proportional to Planck’s Constant? Does it wind up on one end, while unwinding on the other end? Is this related to the Higgs field? Does this help explain the strange ½ spin of many subatomic particles? Does the 720 degree rotation of a 1/2 spin particle require at least one extra dimension?
Alpha decay occurs when the two protons and two neutrons (which are bound together by entangled tubes), become un-entangled from the rest of the nucleons
. Beta decay occurs when the tube of a down quark/gluon in a neutron becomes overtwisted and breaks producing a twisted torus (neutrino) and an up quark, and the ejected electron. The phenomenon of Supercoiling involving twist and writhe cycles may reveal how overtwisted quarks can produce these new particles. The conversion of twists into writhes, and vice-versa, is an interesting process.
Gamma photons are produced when a tube unwinds producing electromagnetic waves.
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Within this model a black hole could represent a quantum of gravity, because it is one cycle of spatial gravitational curvature. Therefore, instead of a graviton being a subatomic particle it could be considered to be a black hole. The overall gravitational attraction would be caused by a very tiny curvature imbalance within atoms. We know there is an unequal distribution of electrical charge within each atom because the positive charge is concentrated within the nucleus, even though the overall electrical charge of the atom is balanced by equal positive and negative charge.
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In this model Alpha equals the compactification ratio within the twistor cone, which is approximately 1/137.
1= Hypertubule diameter at 4D interface
137= Cone’s larger end diameter at 3D interface where the photons are absorbed or emitted.
The 4D twisted Hypertubule gets longer or shorter as twisting or untwisting occurs. (720 degrees per twist cycle.)
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How many neutrinos are left over from the Big Bang? They have a small mass, but they could be very large in number. Could this help explain Dark Matter?
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Why did Paul Dirac use the twist in a belt to help explain particle spin? Is Dirac’s belt trick related to this model? Is the “Quantum” unit based on twist cycles?
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I started out imagining a subatomic Einstein-Rosen Bridge whose internal surface is twisted with either a Right-Hand twist, or a Left-Hand twist. The model grew out of that simple idea.
I was also trying to imagine a way to stuff the curvature of a 3 D sine wave into subatomic particles.
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PHYSICS in St. Finian's College Secondary School Mullingar Co Westmeath Ireland
This is not how it works. Please read Mott's 1929 paper, everybody. The quantum-classical transition is NOT an ensemble effect. It is repeated weak measurement on THE SAME system. One can look at ensembles until the cows come home (even with the density matrix) and classical mechanics won't come out. It's not in there.
What causes classical mechanics to emerge is that the energy loss towards infinity constantly localizes a quantum system with a very large angular momentum. So why do we need repeated observation? Because the transition is caused by CONDITIONAL PROBABILITIES. The system has been localized after the first measurement. From there it can only evolve due to its current momentum, i.e. it can't drift very far until we do the second, third, etc. measurements.
One simply can not get conditional probabilities out of an ensemble in which we only perform one measurement per system. Conditional probabilities require consecutive measurements. The wave function alone is therefor not enough. It represents a single measurement process only.
Instead of talking so much about abstract entities, if you describe a physical process in ordinary life, like growth of a plant or activity of an animal, where the relevant abstract concepts can be applied, then every lay person would understand it clearly.
Remember, the great physicist once said:
If you can't explain it to a six year old, then you don't know what you are talking about.
Demonstrate with a practical application instead of purely abstract concepts.
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@8:30 Says wave cannot be measured. He should go back to school? Seems awfully confused since we are always defining wave lengths of different photons. A "wave packet" he so loves is just a SINGLE Comlete wave. that is all.
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Thank you sir