Thermodynamics, Statistical Physics, and Quantum Mechanics

The probability of spin up is and that of spin down is

b) In the usual NMR experiment, one chooses the field so that

in which case and and The

spin oscillates slowly between the up and down states.

Variational Calculations

5.31 Anharmonic Oscillator (Tennessee)

Many possible trial functions can be chosen for the variational calculation.

Choices such as exp are poor since they have an undesirable cusp

at the origin. Instead, the best choice is a Gaussian:

where the potential in the problem is

We evaluate the three integrals in (A.3.1)–(A.3.4).

We have used (A.3.1) to derive the last expression. Now we find the min-
imum energy for this choice of trial function by taking the derivative with

278 SOLUTIONS