This preview shows page 1. Sign up to view the full content.
Unformatted text preview: ( 1 ) ( ) ( x U x p i x x x op op x = + = + = + h , where op op x op ih p i U + = + = 1 ) ( 1 ) ( h The hermitian operator h op is said to be the generator of the transformation. Finite Spatial Translations: The operator U op (a) that generates a finite spatial translation is given by ) ( ) ( ) ( x a U a x op = + , where h / ) ( ) ( op x op p ia iah op e e a U = = ( U op is unitary since h op is hermitian) Proof: = = = + ) ( ! 1 ) ( ) ( n n dx d a x dx d a n x e a x ( Taylor Series Expansion )...
View Full Document
- Spring '07