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