In problem 2, on the right side of the two equations make the replacements tanhab o tanhDb; cothab o cothDb p. In problem 17, the last term of the last equation should read O 2 2! In problem 4. The final states in both cases should be 1. Degeneracy is usually associated with the existence of mutually commuting observables and this example is no exception. We start with radiation in a cavity at temperature T.
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Quantum Physics - S. Gasiorowicz - 3rd Ed
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The Valence Bond Method The last difficulty can be avoided with the use of the valence bond also called Heitler- London method, in which linear combinations of atomic orbitals are used. We could, in principle, add a triplet term to our variational trial wave function. However, a triplet wave function must be spatially antisymmetric and yields low proba- bility for the electrons being located in the region between the protons. We saw in our dis- cussion of the molecule that just this configuration led to the lowest energy. Although it is not immediately obvious that the attraction is still largest in this configuration when there are two electrons that repel each other in the system, it is in fact so. The results of a variational calculation with the VB trial wave function are This is not a significant improvement over the MO results, for the simple reason that the inadequacy of the trial wave functions for small RAB carries more weight. There should be no question about the quantitative successes of quantum mechanics in molecular physics.