PHYSICS 137A Midterm: physics137A-sp2013-mt1-Debuhr-soln
Document Summary
Physics 137a quantum mechanics spring 2013. A particle of mass m is trapped in an in nite square well of width a, stretching from x = 0 to x = a. Suppose a piece of lab equipment can repeatably produce the following initial conditions for the particle: (cid:19) cos(cid:18) 3e1t where e1 is the ground state energy of the in nite square well. Solution (a) the given initial conditions have already been expanded in the basis of energy eigenfunctions of the in nite square well hamiltonian. So all that is needed to nd the full time dependent solution is to tack on the usual exponential phase factor. If you like, you can trade those en for n2 22/(2ma2). 2(x)e ie2t/. (b) to nd the possible energies that could result from an energy measurement, we have to consider the following application of the third postulate:
