# Expectation value

1. Dec 6, 2005

### asdf1

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

2. Dec 6, 2005

### 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.

3. Dec 6, 2005

### 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.

4. Dec 6, 2005

### harsh

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

- harsh

5. Dec 8, 2005