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Time reversal and motion reversal

  1. Dec 17, 2015 #1
    Does time reversal operation changes the time "t" to time" -t"( For example if we are at t=10 s then by applying time reversal operator the time turns into t=-10 s?), or time reversal operation operates instantly in such a way that if it operates on a ket at t=10 s it only reverses the motion at exactly t=10 s?
     
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  3. Dec 18, 2015 #2

    DrClaude

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    Staff: Mentor

    Could you please specify what you mean by "time reversal operator"?

    What is usually meant by time reversal is that if you have a system in state ##| \psi (t_1)\rangle## at time ##t_1## and evolve it to time ##t_2 > t_1## and find ##| \psi (t_2)\rangle##, then you will find that you can recover state ##| \psi (t_1)\rangle## by evolving state ##| \psi (t_2)\rangle## "backward in time", by simply changing ##t## to ##-t## in the Schrödinger equation. In other words, the TDSE is symmetric with respect to time reversal.
     
  4. Dec 19, 2015 #3
    Time reversal operator is an anti unitary operator ##\Theta## and ## \Theta \psi (x,t)=\psi^*(x,-t)##. Your statement is ##U \Theta \psi(t_2)= \Theta \psi (t_1)## in which ## U ## is time evolution operator and I guess that ## \Theta \psi (x,t)=\psi^*(x,-t)## means instant change of time in reverse direction and not changing t to -t.
     
  5. Dec 21, 2015 #4

    DrDu

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    Science Advisor

    No, the time reversal operator acts on all t.
     
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