Lecture - 8 Quantum Physics

[@tanmaysingal0]

Topics covered: - Inner Product of < x | p > ~ e^{ipx}, - Position Wavefunction Momentum Wavefunction by Fourier Transform. - Generalizing the entire discussion to 3D (was upto 1D till now). - Schrodinger's Equation - separating the time variables out of it by writing down solutions for stationary states. - Time-Independent Schrodinger Equation as an eigensystem equation for the Hamiltonian operator. - Setting up the One-Dimensional Particle in a Box problem (continued in the next lecture).

[@bookofspirit]

Thanks a ton!!

[@saketpanigrahi]

Thanks

[@Rohan_Choudhary5]

Thanks brother

[@bipinsonawane5312]

Please share this series of lectures in all institutes where science is taken seriously.This is the real wealth . This is real need for a student who wish to do science at a deeper level.Thanks all for unexplainable hardword taken to do this work.Of course, Prof. thank you.

[@gouranggehlot4896]

Finally Balakrishnan sir made a mistake at 40:09(it's a relief, he is human too), it's overlap between state at t=0 and the energy eigen state not the position eigen state.

[@sci-informatics3507]

It overlaps with the stationary state. Prof. Balakrishnan describes at 32:00

[@varunshrivastav8876]

@@sci-informatics3507 so he's not human after all

[@ayeshakawakil845]

@@varunshrivastav8876 this professor is blessed with Krishna himself...I am from Rural Bihar and professor literally has turned me to a scientist

[@IamAdarsh1414]

😂

[@UORA75]

The lecturer cleared out lot misunderstood priciples I had. Thank you for the video. I studied all those in Shankar's book but it wasn't so clrear and straight forward for solo-learning.

[@qlw15138]

This is a Master Teacher at work! Great lecture!

[@abhishekpatra3816]

The way he predicted the energy eigenvalues at the end by using bohr's uantization and phase space is so awesome and awestrucking......i have never seen anything like that. Woww......😂😂😂

[@metuphys5611]

that "what the hell" at 40:30 had me weak fr fr

[@frankieli98]

he's so inspiring. I feel like I am in India right now.

[@karthickraja6854]

He is real teacher. That's Inspiring ...

[@mahesh3179]

particle in box 🔥🔥🔥🔥🔥🔥🔥

[@vivekpanchal3338]

Particle in a 1D box starts at 5 50:28

[@sandeeppatidar1106]

Amazing lecture

[@BHA7619]

Thank you Sir, your work is priceless!!

[@GhostFaceK1ll3r]

I love it. Keep it going brother!

[@IamAdarsh1414]

🙏🙏🙏

[@TheManglerPolishDeathMetal]

indeed it is

[@pramod120895]

Can anyone explain coefficient part in 39:59

[@mathieumaticien]

I don't get that either. Did you figure it out? Also how do we even know that we can write the general state Psi as a combination of the eigenstates of the Hamiltonian?

[@pramod120895]

@@mathieumaticien Actually it's overlap between state psi and stationary state phi(n) @ time 0..not with position.. Since stationary states form complete set of eigenkets any vector in Hilbert space can be expanded as linear combination of these states with appropriate coefficients.. Since it is constant hamiltonian stationary state at time t is given by initial state psi n (r, 0) multipled by evolution operator given by exponential of eigen value..

[@mathieumaticien]

@@pramod120895 oh i see that's very simple, you just take the inner product of Psi(t) with Phi_m(t) and use orthogonality of the eigenstates... How does one know Hamiltonians are Hermitian and the spectral theorem is valid?

[@pramod120895]

@@mathieumaticien Hamiltonians are just function of position and momentum operators which are real (mathematically). thus complex conjugate transpose is also same as original operator and thus it is hermitian. (of course it has rigorous mathematical proof) Thus any hermitian operator have complete set of orthonormal eigen vectors with real eigen values and spectral theorem is valid ie sum of (ket(A)*bra(A)) =1 where A's are eigen vectors

[@007acreed]

awesome....sir

[@mikel5264]

If the eigenvalue is the actual value of the physical observable, what is the physical meaning of the eigenstate? Is it a 'vector' of the state of the system with all possible values for that particular observable? Thanks

[@MrNerdpwn]

An eigenstate has no physical meaning. It is an abstract mathematical concept. Only physically meaning things are the eigenvalues of observables and the inner products (probability amplitudes).

[@fazleyahmad8239]

very nice lecture sir

[@20shourya]

@charbi88 r u sure man? not undergrad?

[@tanmaysingal0]

Correction: c_n = < \phi_n | \psi (0) >, not < r | \psi(0)>. (kzbin.info/www/bejne/jJC6f2eYiJ2Zars)

[@navalrsabe7015]

completely, uncertain to me

[@abdulwali2347]

anyone tell me , which book sir follow ?

[@stoksc]

i think it's sakurai from what he's teaching.

[@ashishnayak2020]

Quantum physics by hc verma also states in same manner

[@kumar67749]

God