Find Expectation Value for 1st 2 States of Harmonic Oscillator

[asdf1]

how do you find the expectation value <x> for the 1st 2 states of a harmonic oscillator?

 

[inha]

The expectation value of an operator A is <psi|A|psi>. If you're not familiar with Dirac's notation that means that for state 1 you'd integrate psi1 times A times psi1 over all space.

Once you start getting your hands dirty with the integrations pay attention to wether the integrand is even or odd. That will save you from a lot of useless intergration. Also the gamma function may prove to be useful.

 

[Galileo]

Well, they are $\langle \psi_0|x|\psi_0\rangle$ and $\langle \psi_1|x|\psi_1\rangle$ ofcourse.
You could find them either by integration or the application of the ladder operators.

However, a look at the probability distributions $|\psi_0|^2$ and $|\psi_1|^2$ should tell you immediately what the expectation value for the position is.

 

[harsh]

Well, they are $\langle \psi_0|x|\psi_0\rangle$ and $\langle \psi_1|x|\psi_1\rangle$ ofcourse.
You could find them either by integration or the application of the ladder operators.
However, a look at the probability distributions $|\psi_0|^2$ and $|\psi_1|^2$ should tell you immediately what the expectation value for the position is.

You can do that, but if you really want to see the math, use the ladder operators.

- harsh

 

[asdf1]

ladder operators? what's that?