Question: Consider the integral Where the functions are one-dimensional harmonic-oscillator wave functions with quantum numbers v2 and v1. Under what conditions do parity considerations allow us

Consider the integral

Where the functions are one-dimensional harmonic-oscillator wave functions with quantum numbers v2 and v1. Under what conditions do parity considerations allow us to conclude that this integral must be zero? Might the integral be zero in other cases as well? (This integral is important in discussing radiative transitions.)

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