Group & Phase Velocities of Wave packet in Quantum Mechanics

Group velocity is the velocity of the quantum particle while Phase velocity is the velocity of the wavefunction. They are not equal.
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In quantum mechanics, group velocity refers to the speed at which the peak or envelope of a wavepacket propagates through space. Phase velocity, on the other hand, refers to the speed at which the phase of the wave oscillation moves. In some cases, phase velocity can exceed the speed of light, but it doesn't carry actual energy or information. Group velocity is associated with the movement of the wave packet itself, while phase velocity is related to the oscillatory behavior of the wave within the packet. In quantum mechanics, the evolution of this wave packet is an approximation of the trajectory of the classical particle.
00:00 Introduction to Wave packet
06:15 Dispersive & Non-dispersive Medium
09:45 Group & Phase velocities
26:20 Group Velocity of Particle
37:17 Phase Velocity of Particle
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[@tooclose80]

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

[@diviner524]

Thank you! From someone who also loves physics!

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[@usmanbisola3454]

Your video has been helpful in my quantum mechanics classes. Much love from Nigeria, Africa.

[@harry-ho9ti]

Kindly upload more lectures sir. U r the master piece of teaching profession sir.

[@AlenThomas-xd8kq]

Sir pls keep going,,, plss don't stop this series

[@ItsDeveshA]

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

[@sarbajitsarkar9611]

This playlist is a great gift professor ❤

[@zokru8526]

you have really nice communication with the head nodding when talking about definite contexts

[@aafeer2227]

Simply the best explanation I ever heard. Brilliant. Thank you.

[@TheJara123]

As usual a clear and physics marred to math approach...nicely done man!!

[@anandbavkar8572]

Very Helpful, Thank you very much for all the efforts!!

[@AbdallaDaaMadowe-kn4jq]

A remarkable teaching by a remarkable teacher Thanks a lot sir

[@maheshrocks65-df2mm]

Emversity provides industry-relevant knowledge that sets you apart.

[@YossiSirote]

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?

[@schmetterling4477]

It's a function of space and time, but separation of variables can be achieved for time-independent potentials.

[@rahmatealam3919]

I love your teaching style sir ❤

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U r the best Explainer ❤❤❤❤

[@JohannesK-T]

Thank you, very clear explanation! 😊

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What a great teacher

[@Chiller-wx6gp]

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[@arnabbanerjee417]

Another great video

[@amjadali-lx4lh]

v v v v good lecturer. plz upload soon next video

[@surajyadav607]

Thankyou sir❤

[@parameswarinallusamy3119]

Useful for me

[@SergeyPopach]

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).

[@schmetterling4477]

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.

[@MishaCoolDude]

Nice!

[@sdsa007]

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!...

[@Adrishkar000]

Sir, please discuss about wave properties like interference,diffraction, polarization etc

[@SiddharthSingh-ff2hl]

Sir Plz upload atleast 2 lectures a week for the love of students

[@GoutamDAS-ls1wb]

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?

[@deadman746]

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.

[@FortheLoveofPhysics]

Want to learn how the concept of Wave packet leads to the Uncertainty Relations? kzbin.info/www/bejne/jmXMY5Spq82Dm7s

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Please upload Infinite Square well and Finite Potential

[@Aashu3103]

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.....

[@FortheLoveofPhysics]

For 12th, many topics will be out of syllabus.

[@Aashu3103]

​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 😂....

[@Aashu3103]

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 ❤❤❤❤❤

[@Naman...123]

​@@Aashu3103true , Good to see someone is learning for the sake of Interest ✨💫

[@anandbavkar8572]

@@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.

[@aaliyaali4019]

sir can u make series of ct scan machine physics and also as of mri

[@amjadali-lx4lh]

plz tell plane wave solution of Schrodinger eq is probably amplitude or wave packet is probably amplitude?

[@dominvs935]

please make a scilab tutorial on this.

[@arnabbanerjee417]

One question at 17.55 will that be f(x) or f(x,t)? Very nice video. Thank you

[@AdithyaJonnakuti_07]

W 🔥🔥🔥🔥

[@PriyanshuGupta-hf2hm]

Write a book, sir!

[@loveforallbxlmannif]

Is it different than what we have for sound wave ?

[@schmetterling4477]

With regards to group and phase velocity? No, not really. With regards to what the wave means? Absolutely.

[@bustercam199]

phase velocity is not just an abstract mathematical construction, but we do not have the technology to measure it.

[@schmetterling4477]

Of course we do.

[@bustercam199]

@@schmetterling4477 the phase velocity is a physical quantity and not just an abstract construct.

[@themultitalent]

I am seeing this after my quantum paper exam has ended.. thanks

[@Aashu3103]

Please sir ...😢give answer 😢

[@egnumaangerasa3130]

You are absolutely superb but unfortunately, your video uploading frequency is dissatisfying given our excitement to see your videos

[@arjunsinha4015]

Is this reupload?

[@FortheLoveofPhysics]

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

[@muhammadumairahmad9281]

​@@FortheLoveofPhysicsthanks sir

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