PERT. THEORY FOR Q.M. (NON-DEGENERATE): #3 SECOND ORDER CORRECTION

Hi! Today, we are going to continue studying Time-Independent Non-Degenerate Perturbation Theory. In the previous videos, we obtained the 0th and 1st Order Corrections. In this video, we will derive the 2nd Order Corrections.

Here are some of the ones that I have used for this series of videos and that I think give a very good insight on this topic:

-"Introduction to Quantum Mechanics", (Chapter 7), 2nd and 3rd editions, David J. Griffiths & Darrel F. Schroeter

-"On Quantum Mechanics II", Born, Heisenberg & Jordan

-"Degenerate Perturbation Theory", Jim Branson: https://quantummechanics.ucsd.edu/ph130a/130_notes/node334.html#:~:text=in%20the%20regular%20perturbation%20expansion,eigenvalue%20problem%20will%20be%20solved.&text=If%20there%20are%20n%20nearly,n%20solutions%20to%20this%20equation.

-"Quantum Mechanics", (Chapter VII, Pg 149), Leonard I. Schiff

-"Perturbed Spectra Without (it says here) Pain", Nicholas Wheeler

-"Higher-Order Spectral Perturbation by a new Determinantal Method", Nicholas Wheeler (this is a
summary of the previous article)

-"Perturbation Theory", B. Zwiebach (MIT)

-"Time-Independant Perturbation Theory", Jeremy D. Roberts: http://physics.gmu.edu/~dmaria/590%20Web%20Page/public_html/qm_topics/degenerate/index.html

-"Perturbation Theory (Quantum Mechanics)", Wikipedia: https://en.wikipedia.org/wiki/Perturbation_theory_(quantum_mechanics)

-"The Principles of Quantum Mechanics", (Chapter VII, Pg167), 3rd edition, Paul Dirac

As always, here are the time-stamps of the video:
0:00 Recap: 0th and 1st Order Corrections
2:00 1. Relation for "k" equals to 2
3:22 2. Case 1: Inner product with "ell" equals to "n"
12:10 3. 2nd Order Energy Correction
12:20 4. Case 2: Inner product with "ell" different from "n"
20:40 5. 2nd Order Correction to the Wave Function

I hope that you find this subject as exciting and as fun as I do, and if you do, stick around for future videos!

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