p828ps1 - Physics 828: Problem Set I Due Wednesday, January...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

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

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

Unformatted text preview: Physics 828: Problem Set I Due Wednesday, January 16 at 11:59 PM Note: all problems are worth 10 points unless otherwise stated 1. (20 pts.) In class, I discussed the translation operator, and explained how it can be expressed in terms of the momentum operator p . In this problem, you will consider rotation operators, and show that they can be expressed in terms of components of the angular momentum operator L . Start with a wave function expressed in spherical coordinates as ( r, , ). We now consider a rotation about the z axis by an angle . Let R z ( ) be the operator which has the following effect on the wave function : R z ( ) ( r, , ) = ( r, , ) . (1) (a). By expressing ( r, , ) in a Taylor series about ( r, , ), show that ( r, , ) = exp parenleftBigg parenrightBigg ( r, , ) , (2) and hence that R z ( ) = exp parenleftBigg parenrightBigg . (3) Hence, show that...
View Full Document

This note was uploaded on 07/17/2008 for the course PHYS 828 taught by Professor Stroud during the Winter '08 term at Ohio State.

Page1 / 3

p828ps1 - Physics 828: Problem Set I Due Wednesday, January...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online