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Unformatted text preview: x is conserved! Time Translations: The unitary operator T op (a) that generates finite time translation is given by ) ( ) ( ) ( t a T a t op = + , where t a iaE op e e a T op ∂ ∂ − = = h / ) ( ( T op is unitary since E op is hermitian) Infinitesimal Time Translations: The energy operator is the generator of time translations op op E i T h ε − = 1 ) ( , ( ) > − + < = > ∂ ∂ < >= =< > < → ) ( ) ( lim ] , [ 1 t H t H i t H i H E dt E d i op op h h h If H op is invariant under the time translation t → t +a then [E op ,H op ] = 0 and energy is conserved!...
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This note was uploaded on 05/29/2011 for the course PHY 3063 taught by Professor Field during the Spring '07 term at University of Florida.
- Spring '07