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The wave function
ψ(x) = Bxe-(mω/2h)x2
is a solution to the simple harmonic oscillator problem. (a) Find the energy of this state. (b) At what position are you least likely to find the particle? (c) At what positions are you most likely to find the particle? (d) Determine the value of B required to normalize the wave function. (e) What If? Determine the classical probability of finding the particle in an interval of small length δ centered at the position x = 2(h/mω)1/2. (f) What is the actual probability of finding the particle in this interval?
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