- #1
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Hi,
I was wondering if I could test my understanding on the S-matrix and its role in evolving initial states of systems to final states (after some scattering process has occurred).
Would it be correct to say the following:
Given a system in an initial state [itex] \vert i \rangle[/itex], the final state, [itex] \vert f \rangle[/itex] of the system, at a sufficiently long time after some scattering process can be mapped to by the so-called S-operator, [itex]S=\lim_{t\rightarrow\infty,\,t_{0}\rightarrow\infty} U\left(t,t_{0}\right)[/itex] (where [itex]U[/itex] is the unitary time-evolution operator) i.e.
Is it then correct to say that the S-operator annihilates the initial state [itex] \vert i \rangle[/itex] and creates the final state [itex] \vert f \rangle[/itex]?
Also, would it then be correct to say that the S-matrix element [itex] \langle f\vert S\vert i \rangle[/itex] corresponding to the given scattering process gives the vacuum expectation values (v.e.v) for the appropriate annihilation and creation operators involved?
Sorry for any inaccuracies, hoping to gain a more in depth understanding of the concept. Thanks in advance!
I was wondering if I could test my understanding on the S-matrix and its role in evolving initial states of systems to final states (after some scattering process has occurred).
Would it be correct to say the following:
Given a system in an initial state [itex] \vert i \rangle[/itex], the final state, [itex] \vert f \rangle[/itex] of the system, at a sufficiently long time after some scattering process can be mapped to by the so-called S-operator, [itex]S=\lim_{t\rightarrow\infty,\,t_{0}\rightarrow\infty} U\left(t,t_{0}\right)[/itex] (where [itex]U[/itex] is the unitary time-evolution operator) i.e.
[itex]\vert f \rangle=S\vert i \rangle[/itex]
Is it then correct to say that the S-operator annihilates the initial state [itex] \vert i \rangle[/itex] and creates the final state [itex] \vert f \rangle[/itex]?
Also, would it then be correct to say that the S-matrix element [itex] \langle f\vert S\vert i \rangle[/itex] corresponding to the given scattering process gives the vacuum expectation values (v.e.v) for the appropriate annihilation and creation operators involved?
Sorry for any inaccuracies, hoping to gain a more in depth understanding of the concept. Thanks in advance!