Physics H190, Spring 2002

Homework #1; due: Feb. 13

  1. Estimate the root-mean-square (rms) value of (R-Re), where R is the interatomic separation, and Re is its equilibrium value, for a diatomic molecule in a low vibrational state. Hint: use, e.g., the approach we employed in class to estimate the characteristic values of electronic, vibrational, and rotational frequencies.

  2. Examine the explicit form of the spherical harmonics YJM for J=0,1, and 2. Verify that the symmetry of these functions with respect to the rotation of the coordinate frame by p around the x-axis (so that x->x, y->-y, and z->-z) corresponds to (-1)J. Hint: first determine the effect of the transformation on the angles J, j.

  3. Do you agree with the statements made in the last-but-one paragraph on p. 13 of J. M. Brown's book? If not, formulate and prove a related correct statement. Hint: see, e.g., Sec. 86 (Symmetry of molecular terms) in the Landau and Lifshitz QM book. This problem was also discussed in class.