How do a and a^\dagger transform under time reversal transformation?

In summary, the operator a remains unchanged under a time reversal transformation, while the operator a^\dagger changes sign and becomes -a^\dagger. The commutation relation between a and a^\dagger remains unchanged. The time reversal transformation is unitary and changes the sign of all physical observables.
  • #1
wdlang
307
0
it is know that x goes to x while p goes to -p under time reversal transform

so a=x+ip whill transform to a=x-i(-p)=x+ip=a?

so a^\dagger to a^\dagger?
 
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  • #2
Indeed. You have

x = (a^dagger + a)/2
p= i(a^dagger - a)/2

which transform to x and -p if a and a^dagger are fixed by time inversion.
 

Related to How do a and a^\dagger transform under time reversal transformation?

1. How does the operator a change under a time reversal transformation?

The operator a remains unchanged under a time reversal transformation.

2. What happens to the operator a^\dagger under a time reversal transformation?

The operator a^\dagger changes sign under a time reversal transformation, becoming -a^\dagger.

3. How does the commutation relation between a and a^\dagger change under a time reversal transformation?

The commutation relation between a and a^\dagger remains unchanged under a time reversal transformation.

4. Is the time reversal transformation unitary?

Yes, the time reversal transformation is unitary, meaning that it preserves inner products and norms.

5. What is the effect of a time reversal transformation on physical observables?

A time reversal transformation changes the sign of all physical observables, indicating a reversal in the direction of time.

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