Thermodynamics, Statistical Physics, and Quantum Mechanics

One can exchange the order of integration in one of the integrals and

demonstrate that it is identical to the other. We evaluate only one and

multiply the result by 2:

This completes the integrals. The total ground state energy in Ryd-

bergs is

We find the minimumenergy by varying Denote by the value of
at which is a minimum. Setting to zero the derivative of with
respect to yields the result The ground state energy is

Perturbation Theory

5.38 Momentum Perturbation (Princeton)

The first step is to rewrite the Hamiltonian by completing the square on
the momentum operator:

The constant just shifts the zero of the momentum operator. The rewrit-
ten Hamiltonian in (S.5.38.1) suggests the perturbed eigenstates:

QUANTUM MECHANICS 287