PLEASE SHOW ALL WORK A particle of mass m in an infinite, one-dimensional square

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PLEASE SHOW ALL WORK

A particle of mass m in an infinite, one-dimensional square well potential ("particle in a box") of size L is in a superposition of the ground state and the second excited state. We find that it is three times as likely to be found in the second excited state as it is in the ground state. a) If we measure the energy of the particle, what possible values will we obtain, and with what probability? b) Explicitly write the wavefunction for the particle: Y(x,0) at time t 0 and Y(x, t) at a generic time t c) What is the particle's time-dependent probability density function? Express it in such way that it is obvious it is a real function, and comment on its time dependence. d) What would be the average of energy measurements for a large number of identically pre- pared, independent systems of the type described above

Explanation / Answer

For the 1-dimensional case on the x-axis, the

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