Question

Consider the following wave function: Psi(x,t) = Asin(2piBx)e^(-iCt) for 0<x<1/2B Psi(x,t) = 0 for all other...

Consider the following wave function:

Psi(x,t) = Asin(2piBx)e^(-iCt) for 0<x<1/2B

Psi(x,t) = 0 for all other x

where A,B and C are some real, positive constants.

a) Normalize Psi(x,t)

b) Calculate the expectation values of the position operator and its square. Calculate the standard deviation of x.

c) Calculate the expectation value of the momentum operator and its square. Calculate the standard deviation of p.

d) Is what you found in b) and c) consistent with the uncertainty principle? Explain.

2. Show the time derivative of the expectation value of momentum is equal to (up to a minus sign) the expectation value of the x-derivative of the potential energy.

Thank you!

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