Wavefunction & Normalization EXPLAINED

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What is a wavefunction in Quantum Mechanics? Does it have a physical significance? How do we know whether a given wavefunction is physically acceptable or not? Let's discuss all these questions in today's lecture.
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In quantum mechanics, the wave function is a fundamental concept that describes the quantum state of a particle or a system of particles. It is usually denoted by the symbol ψ (psi) and is a mathematical function that provides the probabilities of the outcomes of different measurements on the system. The wave function is a complex function, meaning it can take on complex values, and its absolute square, |ψ|^2, gives the probability density of finding the particle(s) at a given place and time.
The behavior and evolution of the wave function are governed by the Schrödinger equation, a key equation in quantum mechanics. The equation is time-dependent in general, showing how the wave function changes over time. The wave function is not directly observable; instead, its role is to predict probabilities and expectation values of physical quantities in a quantum system.
00:00 What is a Wavefunction?
09:16 Conditions for a physically acceptable ψ
19:11 Exercise - Which wavefunctions are allowed?
24:20 Normalization of a Wavefunction
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Пікірлер: 37

@FortheLoveofPhysics 6 ай бұрын

Upcoming Batches at Elevate Physics IIT-JAM 2025, TIFR & JEST Batch starting JUNE 22 CSIR-NET DEC 2024 & GATE-2025 Batch starting JUNE 30 Find all details here: Website ► www.elevateclasses.in/ Android ► bit.ly/3zU71ur iOS ► apple.co/3ZPRWVJ (use ORG code - AHGXS)

@sumanc76 7 ай бұрын

Sir your teaching is so methodical ! Without the help of any modern gadget , just with chalk and duster you make your lectures so attractive. Really your lectures series is an asset to every physics loving individual.

@Valsula69 6 ай бұрын

I just started quantum mechanics this semester and your explanations make these topics much easier to digest mathematically and visually. Thank you.

@AbdallaDaaMadowe-kn4jq 7 ай бұрын

Thanks great teacher Your beautiful explanation ❤ Keep going 💪

@SergeyPopach 2 ай бұрын

A wave function is some sort of vector space with infinite dimensions, but it encodes information in terms of a magnitude and phase (that's why it is a complex-valued function). This duality of magnitude and phase within Ψ encapsulates the duality of quantum mechanics itself. The magnitude of Ψ encapsulates measurable quantities related to particle's behaviour. The phase of of Ψ encapsulates the intricate quantum behavior of the system, which is related to wave's behaviour.

@kaustabhgautam69 2 ай бұрын

Thank you sir. Very helpful

@user-bi1ky8se8q 4 ай бұрын

Please keep up the good work. I enjoy your class so much

@gregoriogutierrezaranibar262 Ай бұрын

Beautiful explanation, thank you so much.

@anjali7396 2 ай бұрын

Awesome explanations💫.... You explain everything very clearly and in simple language ....its very helpful to understand QM in depth..🤍🤍

@mariocesarsousa 7 ай бұрын

Excellent explanation. Little by little i get the phylosophy.❤

@fredericopires7659 2 ай бұрын

Very good!!

@sombiryadav5043 7 ай бұрын

Excellent 🎉

@alokkumaryt 7 ай бұрын

Excellent explaining.🥰 We need full QM

@anirbanmukhopadhyay6902 7 ай бұрын

Yes, we need full QM.

@ajithg796 7 ай бұрын

Excellent.🎉 Digital Clear concept presentation. No. 1 in the world. No doubt. After watching your classes, I imitated your method of teaching

@muhammadrashidmuhammadrash2585 7 ай бұрын

So greatful sir❤

@labibsoufiane8987 7 ай бұрын

Thank you very mutch

@axona3gaming 7 ай бұрын

thank you sir

@lajuelar 7 ай бұрын

I alway follow your lectures sir.

@amitkumaryadav-ft3in 7 ай бұрын

❤❤ thanks sir

@ujalamarjan 7 ай бұрын

Thnkuuu sir

@user-pb7km3tz8o 7 ай бұрын

Thank from CUTN

@YossiSirote 7 ай бұрын

At 10:50 or so you say the psi cannot be infinite, actually we allow a Dirac delta function which is infinite at a point, but integral over that point is 1. Similarly, we can have it be not continuous using delta functions. At 14:40 or so you talk about normalizable, actually we use no normalizable psi’s all the time when we talk about free particles, we then take collections of these to make normalizable wave packets. But non normalizable psi’s are used in QM all the time.

@FortheLoveofPhysics 7 ай бұрын

I think I have tried to emphasize on the video (maybe I need to do it more) that there's the THEORY of QM, and then there's actual physical systems and quantities. As I mentioned it many times while discussing the "conditions for a ((physically)) acceptable wave function solution", not all solutions of the SE makes "physical" sense. That does not mean that they might not have "mathematical" relevance! Dirac Delta functions are extremely useful, however, There is NO physical system whose solution is a straight forward dirac delta wave function solution. (it would violate the HUP, as in such a situation the momentum of such a particle will be infinite) Same with FREE particle - the solutions are non-normalizable, hence we introduce the Wave-packet approach (if they were acceptable solutions, we wouldn't need to introduce the wave-packet approach now, would we?). Again, that doesn't mean they are useless. While studying scattering, we can use them to get an idea about reflection/transmission/tunneling etc, but individual separable solutions can NEVER be used for a physical particle. Just because mathematical solutions have relevance in the context of the QM theory, doesn't mean they can be used for physically acceptable solutions. I think you are smart enough to understand this distinction.

@rushikanagla690 7 ай бұрын

In example 2 , can I give one more reason that it's not allowed bcz curve has possibility that it's derivative may go to infinite as vertical tangents r also possible ??? Or shall I just consider ur one reason of multiple valued function ,????

@rahulsarma6250 7 ай бұрын

Do you have any batch for iit jam physics

@antontabjopko6434 6 ай бұрын

I tried to leave comment on your special relativity video where you let phi be the angle between the ct and ctprime axis but was not able too. Sorry for posting here but there is a mistake there. You state there tanh phi = beta but this is incorrect. It should state tan phi = beta because when beta is 1 then phi is pi/4. Using your formula phi is infinite for this case. Nevertheless your formula cosh phi = gamma is correct. So tan phi works for angles and tanh phi works for lengths.