Chemistry 3730 assignment 5

Due: Friday, Oct. 10, 10:00 a.m.

1. Calculate the probability that a particle in a box is located between x=L/3 and x=L/2 for n=1 and n=2. Report your answers as floating-point numbers. Explain the difference in the probabilities.
2. Show that the n=3 and n=212 states of the particle in a box are orthogonal by an explicit calculation. Explain why the calculation was a waste of time.
3. Suppose that an electron is held in a one-dimensional box of length L. An electric field produces a potential energy

   

   within the box. Compute an approximation to the energies of the n=1 and n=2 levels of this system. In a spectroscopic study, would a more or less energetic photon be required to induce a transition between these levels than in the absence of the electric field?

4. For a particle in a square two-dimensional box of side L, the wavefunction is of the form

   

   Note that the box is assumed to be in the conventional location, i.e. in the positive quadrant with edges touching the x and y axes.

   1. Calculate the probability that the particle is in the square defined by , in the , and , states. Give your answer in floating-point form.
   2. Calculate the average of in the , state.