What is Uncertainty Principle? Wave Packet Approach - Fourier Transforms of Position/Momentum space
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- เผยแพร่เมื่อ 20 ก.ค. 2024
- A complete and detailed explanation of the Uncertainty Principle using the Wave packet Approach - the Fourier transform of a wave packet in position and momentum space and correlating their spread/ uncertainties.
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The uncertainty principle in the context of quantum mechanics is a fundamental concept that was formulated by Werner Heisenberg. It states that there is a limit to how precisely certain pairs of complementary properties of a quantum system, such as the position and momentum of a particle, can be simultaneously known. In other words, the more accurately you know one of these properties, the less accurately you can know the other.
The uncertainty principle is essential when dealing with wavepackets. As you try to make a wavepacket more localized in position (to know the particle's position more precisely), it will spread out in momentum space (due to its Fourier Transforms), leading to greater uncertainty in the particle's momentum. Conversely, if you want to know the momentum of a particle more precisely (by creating a more focused wavepacket in momentum space), its position uncertainty will increase.
In summary, the uncertainty principle in quantum mechanics, when considered in the context of Fourier transforms and the wavepacket approach, highlights the inherent trade-off between knowing a particle's position and momentum with high precision. It's a fundamental constraint in the quantum world and has significant implications for the behavior and description of quantum systems.
00:00 Introduction to Wave packet Approach
05:07 Fourier Transforms
12:40 Position & Momentum Space
28:35 Inverse Proportionality between Δx and Δp
35:06 Gaussian Wave packet
43:49 Heisenberg's Uncertainty Relations
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Now let's learn about some bizzare consequences of Quantum Mechanics that we can directly show using the Uncertainty Principle th-cam.com/video/DkYmy2MjyzM/w-d-xo.html
Better than all of my teachers in university, you've connected so many of the topics I've been gruesomely studying the past 2 semesters with no explanation as to why. Thank you!
which unviersity?
He's very good at it
Thank you for teaching me. I’m a university student in New York and you are a much better teacher
Sir you are one of the gems when it comes to the teaching domain . Hats off to your teaching style
Excellent teaching ability you have . One of the best teachers on TH-cam platform.
The Best
I understand the wave packet now and underlying uncertainty in that😮😮😮.
Thank you sir ❤❤
My doubt clarified after 15 years with this video thank you sir.. a wonderful class about wave packet and uncertainty principle.
Thank you once again..
Your video lectures make us genuiely enjoy the concept and those concepts no longer appear burdensome to us
you're truly a god for me sir. Thank you so much for this wonderful lecture
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Simply brilliant, you elaborate on those points that are precisely needed to understand the topic. Thanks
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We can successfully fulfill a particle nature and physical quantities, within a limit, a relationship .
As you have demonstrated a black body emissions shape these interesting features . No guarantee a microscopic world with double slit superposition is natural and physical quantities a Physics.
Thank you.
Pranam .
I haven’t seen such quality work in a long time. Great job!
Wow, thanks! :)
sir please increase the frequency of the lectures as the prior videos by you are part of Modern physics in our university and the real quantum mechanics course in our uni starts from Schrodinger equation. I know as a professor you have responsibilities but I am very fond of your lectures and totally dependent on them. sir, please tell me if u need any help from us as your subscribers and students we are ready to help you.
Finally. The topic I was waiting for from you sir. You're a better explainer
Sir you should also do a podcast on the lifestyles of a physicist or a physics educator as yourself to shed a light on how you hard you're working, the methods and lengths you go to researching and studying all these topics to give us such crisp and easy to understand videos ! Maybe give out a blue print so that we may be able to follow your foot steps ! Absolutely loving the way you're teaching physics in such an unconventional manner ! You are unlike any other teacher on the internet especially Indian teachers who are so focused on teaching, keeping the objective of attaining good marks in mind that they fail to teach us in such a way that it leaves a lasting impression on the brain ! My only regret with this channel is that, I may have found it a year or two, too late ! I will be dropping Physics and will start preparing for gov jobs ! However watching your videos might just be included in my long list of hobbies now ! Sir I wish you nothing but the very best ! God Speed !
Muchas Gracias Doctor ! Su manera de explicar es Excelente !
SIR I HAVE AGAIN GOT MYSELF INTERESTED IN PHYSICS DUE YOUR EXPLANATIONS OF THE NATURE'S BEHAVIOUR
THANK YOU SIR VERY MUCH
Excellent video. Congratulations and thank you !
Beautifully explained!
Sir, BIG THANKS !! You should win Nebel prize for teaching.
Also this particular video deserves much more views
Very helpful sir....may your works progress more🙏
Thanks sir , wonderful explaination ❤. Actually can you suggest books for integral calculus.
This video was exactly what I have been looking for in along time. Now I finally gets it .. thank you sir ! Now I can sleep tonight😅
i simply love the way you have covered the uncertainty principle. Can we also get the essence of this principle via linear algebra? for example talking about how the moment we represent the multidimensional vector space in terms of position basis states and the change the basis to momentum basis states etc?
Thank you!! You've helped me a lot
This man> my all University teachers
Great lecture !
Emversity's instructors are dedicated to your success and development.
Excellent Lecture. Please proceed so.
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sir very thanks to you ,
please cover Schrödinger eqn as I have my mid sem on 19oct
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Best explanation ❤
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Sir please upload schordinger wave equation vdeo
32:20
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Double times thanks sir. You're explaining the real Quantum mechanics and others are trying to just cover the course somehow.
Sir, can you do a video on Klein-Gordon Equation ?
Sir please make a video on the entropy❤
Can you, please, derive this kind of inequality of uncertainty for energy and time? As momentum is directly related to wave number k thru Planck's constant, p=hk (so, you can perform Fourier transformation and inverse it between momentum and position). Simuarly, this can be done between energy and time, since energy is directly related to angular frequency, E=hw (so, you can perform Fourier transformation and inverse it between frequency and time). Note that this uncertainty describes how fast the quantum system evolves with time for given number of egienstates (energy basis).
Sir I have this one question related to the displacement of a body when force is applied on it.
So the question goes like this :-
There is a boy travelling with a cycle and while travelling he throws a ball in upward direction (against gravity) but at the same time when boy is throwing ball he is also cycling due to which it happens that, the position of the boy when he threw the ball and the position of the boy when he caught the ball was different. The position in which the ball is caught is slightly ahead of the position in which the ball is thrown and the positions of both are different. Now basically when the position of the boy (along the cycle) has been displaced or it has been recoiled and then when we are applying force to the ball in a particular direction (meaning upward) then why is the ball back in our hands?Since we have already recoiled. So does it mean that the force we are applying is causing the displacement of ball in two directions, one towards the upward direction and one towards the direction in which boy is cycling.
Sir it could be a weird question for you but as a 10th grader I'm struggling in it. Maybe I haven't clear my motion basics. It would be very much helpful if you answered it
The position of the ball should not change unless the cycle accelarates. If the position of the ball when caught is slightly ahead , then the cycle must have slowed down. (Don't consider air resistance)
@@pingtexelite3914 Thankyou for your answer, but the speed was constant throughout the path
I think sir could explain it then .
@@pingtexelite3914 Thakyou because you gave a conclusion
Welcome ❤
at 46:42 why divided by 4 pi, why not 100000 pi or 1.2 pi? does the principle even have the theoretical base or was it just from experimental observations? i cant be from observations because it specifically says 4 pi.
Excellent sir love from Pakistan🇵🇰❤
At 39’46”, why is the ratio equal to exp(-1/2) instead of 1/2 ?
Because the denominator exponential will be equal to 1.
And because he choses the FWHM of the Gaussian at the same particular width to maintain the consistency. It is an arbitrary step, but it is irrelevant to the final result.
pdf scanned copy is missing, please upload it.
Video is private?
❤
Hello sir ❤how are you
In the first part of the video, we calculated that k = P multiply by h dash . Now we are saying k = P divided by h dash. Please I need clarity on that
P = h dash multiple by k
Sir in which institute you are working now
Hansraj
Sir please make video on physics of tantra mantra and physics of magic
I think you limit yourself with the mathematics. You should assume that we are familiar with Fourier Transforms and that we can do complex integrals. Your definition of Δx is not the standard deviation as is the usual definition. I think more advanced maths would bring this series further.
If you're so smart, why do you need this? Many other highly technical presentations you could view that give you no intuition as to what you're doing other than shutting up and calculating. This channel is for the common man. That's why it's called For the LOVE of physics...
Quantum physics has no rules 😭 anything can happen 😅
Excellent!