Unformatted text preview: ( 1 ) ( ) ( x U x p i x x x op op x ψ = + = ∂ ∂ + = + 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: ∑ ∞ = = Ψ = + ) ( ! 1 ) ( ) ( n n dx d a x dx d a n x e a x ( Taylor Series Expansion )...
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This note was uploaded on 05/29/2011 for the course PHY 4064 taught by Professor Fields during the Spring '07 term at University of Florida.
- Spring '07