Thermodynamics, Statistical Physics, and Quantum Mechanics

At time we start in state Later this state becomes

The amplitude for pointing in the negative is found by taking

the matrix element with The probability is the square of the absolute

magnitude of this amplitude:

5.30 Nuclear Magnetic Resonance (Princeton, Stony

Brook)

a) Let and denote the probability of spin up and spin down as a
function of time. The time-dependent Hamiltonian is

The equations for the individual components are

where the overdots denote time derivatives. We solve the first equation for
and substitute this into the second equation:

276 SOLUTIONS