Calculate the mean displacement of the harmonic oscillator, Ask an Expert

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2) A) Calculate the mean displacement of the harmonic oscillator when it is in a quantum state ?. Use the Hermite polynomials in the attachment and the recursion relation to justify your answer through symmetry arguments.

B) Find the maximum probability density of the ?=1 state?

4) What is the most probable point at which an electron in a 2pz-orbital will be found? What is the probability of finding an electron within a sphere of radius R centered on the nucleus?

5) Show that the standard deviation ?A is 0 when ? is an eigenfunction of A

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