- #1
syhpehtam
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Hi guys, I am reading Ballentine's Quantum Mechanics book, and I am stuck on p.77.
In this page, there is also a sentence that I don't understand:
I don't know how the above formula comes, what is the effect of [itex]e^{isH}[/itex] when it acts on a vector?Corresponding to the time displacement [itex]t\rightarrow t'=t+s[/itex], there is a vector space transformation of the form (3.8),
[tex]
|\Psi(t)\rangle\rightarrow e^{isH}|\Psi(t)\rangle=|\Psi(t-s)\rangle.
[/tex]
In this page, there is also a sentence that I don't understand:
Does this sentence imply something that can derive the above formula?The dynamics of a free particle are invariant under the full Galilei group of space-time transformations, and this turns out to be sufficient to completely identify the operators for its dynamical variables.