M402-set.8.soln.f10.ver2

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

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

View Full Document Right Arrow Icon
Background image of page 1

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

View Full DocumentRight Arrow Icon
Background image of page 2
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
Background image of page 3

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

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

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 Right Arrow Icon
Ask a homework question - tutors are online