1) Consider the following example of a quantum mechanical wavefunction for a particle of mass m...

1) Consider the following example of a quantum mechanical wavefunction for a particle of mass m moving in one dimension, where α and A are constants.
?(?, ?) = ?? − ?(?2 + ?ℏ?/?) ,

a) Normalize the wavefunction. Show your work.

b) At what value of x is there equal probability for the particle to be either to the left or to the right of that x? Show your work and explain.

c) For the wavefunction given, what must the potential V (x, t) be in order for Ψ(x, t) to satisfy the Schrodinger equation? What classical system has this kind of potential?

d) Calculate the expectation values of x, x2, p, and p2. Explain in words what each calculation means (how it is related to measurement).

e) Determine ?! and ?" and check if their product is consistent with the uncertainty principle.

Expert Solution

genius_generous answered 1 year ago

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