Thermodynamics, Statistical Physics, and Quantum Mechanics

324 SOLUTIONS

This is the eigenvalue equation which determines as a function of param-

eters such as D, etc. In order to find the range of allowed values of

D for bound states, we examine The right-hand side of (S.5.71.9)

goes to 1, which is its largest value. So, the constraint for the existence of

bound states is

5.72 Ionizing Deuterium (Wisconsin-Madison)

The ionization energy of hydrogen is just the binding energy of the electron

which is given in terms of the reduced mass of the electron–proton

system. The same expression for deuterium contains the reduced mass

of the electron–deuteron system:

The difference is easily evaluated. The ratio is a small number and

can be used as an expansion parameter:

The ratio of masses gives and

5.73 Collapsed Star (Stanford)

a) Using the 1D Schrödinger equation