- #1
qtm912
- 38
- 1
This question concerns the outcome when operator valued functions act on an energy eigenstate. Given an eigenstate at t =0, say |Ej > , I have seen or inferred in some of the literature that the following applies :
exp(-iHt/h) |Ej > = exp(- iEj t/h) |Ej >
Where h = h-bar
Ej is energy eigenstate j
H is the Hamiltonian
I am unclear in particular why we can say that if we apply a function with an operator as the argument to this energy eigenstate, it will return the function with the eigenvalue as the argument times the energy eigenstate. (assuming I have inferred what is in the notes correctly)
Would this then be a general result for all functions or do only certain functions satisfy this relationship. (So for example would it be true for sin(H) instead of exp(-iHt/h) )?
exp(-iHt/h) |Ej > = exp(- iEj t/h) |Ej >
Where h = h-bar
Ej is energy eigenstate j
H is the Hamiltonian
I am unclear in particular why we can say that if we apply a function with an operator as the argument to this energy eigenstate, it will return the function with the eigenvalue as the argument times the energy eigenstate. (assuming I have inferred what is in the notes correctly)
Would this then be a general result for all functions or do only certain functions satisfy this relationship. (So for example would it be true for sin(H) instead of exp(-iHt/h) )?