One classic problem in quantum mechanics is the harmonic oscillator. In this problem a particle is subjected
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One classic problem in quantum mechanics is the “harmonic oscillator.” In this problem a particle is subjected to a one-dimensional potential (taken to be along x) of the form V (x) ∝ x2, where −∞ ≤ x ≤ ∞. The probability distribution function for the particle in the lowest-energy state is:
P (x) = Ce-ax2 / 2
Determine the expectation value for the particle along x (that is, x). Can you rationalize your answer by considering the functional form of the potential energy?
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The last equality arises from x being an odd function whi...View the full answer
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