- #1
Jomenvisst
- 7
- 0
So, this has been bothering me for a while.
Lets say we have the wavefunction of a harmonic oscillator as a general superposition of energy eigenstates:
[itex]\Psi = \sum c_{n} \psi _{n} exp(i(E_{n}-E_{m})t/h)[/itex]
Is it true in this case that <V> =(1/2) <E> .
I tried calculating this but i get something like
<V> = < [itex]\Psi |V| \Psi [/itex] > = (1/2)<E> + some other term that does not seem to be zero generally.
However, it seems to me that <V> =(1/2) <E> should be true even in this case, since
[itex] <V>_{n} = <\psi_{n} | V | \psi_{n} > = (1/2) <E> [/itex] for every n.
Lets say we have the wavefunction of a harmonic oscillator as a general superposition of energy eigenstates:
[itex]\Psi = \sum c_{n} \psi _{n} exp(i(E_{n}-E_{m})t/h)[/itex]
Is it true in this case that <V> =(1/2) <E> .
I tried calculating this but i get something like
<V> = < [itex]\Psi |V| \Psi [/itex] > = (1/2)<E> + some other term that does not seem to be zero generally.
However, it seems to me that <V> =(1/2) <E> should be true even in this case, since
[itex] <V>_{n} = <\psi_{n} | V | \psi_{n} > = (1/2) <E> [/itex] for every n.