J.J. Sakurai Modern Quantum Mechanics p. 74(adsbygoogle = window.adsbygoogle || []).push({});

It says,

[A,H] = 0;

H|a'> = E_{a'}|a'>

where H is the Hamiltonian A is any observable |a'> is eigenket of A

then,

exp ( -iHt/h)|a'> = exp (-iE_{a'}t/h)|a'>

where h is the reduced planck's constant.

I want to know WHY ?

and besides, I would like to ask what is generating function means?

I have encountered

x_{new}=x+ dx

p_{new}=p

then generating function for infinitesimal translation is

F(x,P) =x·P+p· dx

How can I understand it ?

Thank You ! I wish this time is readily to read !

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# Operator in exponential function and generating function

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