Find Expectation Value for 1st 2 States of Harmonic Oscillator

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how do you find the expectation value <x> for the 1st 2 states of a harmonic oscillator?
 
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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.
 
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.
 
Galileo said:
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
 
ladder operators? what's that?
 
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