M402-set.8.soln.f10.ver2

# M402-set.8.soln.f10.ver2 - Problem Set 8 Fall 2010...

This preview shows pages 1–4. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Problem Set 8 Fall 2010 Solutiuon to Problem 3 . a) Show that a solution to ħ 2 2 m 2 F r EF r is given by F r l , m a l , m j ar Y , m , where 2 mE / ħ 2 1/2 . Solution : First we note that the differential equation can be written: ħ 2 2 m 2 E F r 0 2 2 F r 0 1 r 2 d dr r 2 d dr L L ħ 2 r 2 2 F r , , 0 Multiplying by r 2 and noting separation of variables can be made in r and the angular dependence: F r , , h r Y , 1 h r d dr r 2 d dr 2 r 2 h r 1 Y , L L ħ 2 Y , ℓ ℓ 1 where ℓ 1 is the separation constant. The right hand side we have solved in the notes and gives: L LY , m , ħ 2 ℓ 1 Y , m , where

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 12/20/2010 for the course PHYS 402 taught by Professor J. during the Fall '09 term at Missouri S&T.

### Page1 / 4

M402-set.8.soln.f10.ver2 - Problem Set 8 Fall 2010...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online