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Schordinger's Equation-Mathematical Physics-Assignment, Exercises of Mathematical Physics
This assignment is for Mathematical Physics course. It was assigned by Dr. Akshat Nair at Central University of Odisha. It includes: Schrodinger, Equation, Boundary, Conditions, Quantum, Particle, Sturm-Liouville, System, Eigenvalues, Normalized
Typology: Exercises
2011/2012
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Mathematical Physics, PAM -507 M.Phil(Physics) (Final Examination, April 04, 2011) Total marks 100 Exam duration 3.0 hours / Question 1. The Schrodinger equation and boundary conditions for a quantum particle in one dimensional space are given by: h* d*w(x) _ om dx2 — E(x) =0 (0) =0 pL) =0 This is a regular Sturm-Liouville system. (a) Find the eigenvalues and eigenfunctions also J (b) Find the normalized eigenfunctions Question 2. The generating function for Legendre’s polynomial is given as = l @(x, h) = Pi(x)a' = 0) 2 V1-2xh+h Show that GPi(x) dPi-1(x) (a) x ~ — = “! = IP,(x), where € =1, 2,3... / (b) If Pax)= — (6435 x®-12012 x°+ A -1260 x2+35) Find the missing term givenbyA = & qink (17) (08) (17) (08) docsity.com