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Initial state vector
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Your fun to be this community has been maintained. Problem 1. The first term integrates to zero, using integration by parts twice, and the second term can be simplified to. Proof: This has no effect on the expectation value of a dynamical variable, since the extra phase factor, being independent of x, cancels out in Eq.
In view of Eq. So for a given value of y, the probability of crossing using Problem 1. In particular, since solutions. Problem 2.
By the same token, if it starts out heading negative, it just runs more and more negative. These results hold for any stationary state of the harmonic oscillator. From Eqs.
But, noting that and using Eqs.