PHYSICS 137A Midterm: physics137A-fa2012-mt1-Debuhr-soln
Document Summary
Physics 137a quantum mechanics fall 2012. Consider the in nite square well of width a (extending from x = 0 to x = a). Take the initial spatial wave function to be a parabola centered around the middle of the well: Xi=1 cn n(x) where cn are some constants and n(x) are the energy eigenfunctions. Set up a calculation of the coe cients, cn, and write it as an integral with everything spelled out explicitly; you do not have to evaluate the integral. Solution (a) the normalization condition for this wavefunction is the following. These are straightforward integrations to perform so we nd. Note that we could have multiplied this by a phase factor, but we chose to have a real value for a. (b) the expectation value of p is given by the following: hpi = z a. This is a case where we can jump to the answer.
