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One dimensional Quantum Mechanics problems

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1.
A particle of mass m moves in one dimension in an infinite square well. Suppose that at time t=0 its wave function is

Psi(x,0) = A[(L/2)^2-x^2]

a. Find the probability of obtaining value En of the particle energy where En is one of the energy eigenvalues
b. Determine the expectation value <E>. What is the probability that the particle's energy at t=0 is equal to teh expectation value?
c. What is psi(x,t)

2.
Consider the potential V(x) = -a*V0*delta(x-L) - a*V0*delta(x+L)
Find the bound states and their wavefunctions.

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The 16-page solution gives a detailed step-by-step explanations to the two problems regarding a particle mass in one dimension.

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