Thermodynamics, Statistical Physics, and Quantum Mechanics

63

At the system is instate Derive the probabilitythat at any

later time it is in state

5.29 Rotating Spin (Maryland, MIT)

A spin-1/2particle interactswith amagneticfield through the

Pauli interaction where is the magnetic moment and

are the Pauli spin matrices. At a measurement determines

that thespin ispointing along the positive What is the probability

that it will be pointing along the negative at a later time

5.30 Nuclear Magnetic Resonance (Princeton, Stony

Brook)

A spin-1/2 nucleus is placed in a large magnetic field in the

An oscillating field ofradiofrequency isapplied in the

so the total magnetic field is

The Hamiltonian is where is the magnetic moment. Use the

notation

a) If the nucleus is initiallypointing in the at what

is the probability that it points in the at later times?

b) Discuss why most NMR experiments adjust so that

Variational Calculations

5.31 Anharmonic Oscillator (Tennessee)

Use variational methods in one dimension to estimate the ground state

energy of a particle of mass in a potential

5.32 Linear Potential I (Tennessee)

A particle of mass is bound in one dimension by the potential
where F is a constant. Use variational methods to estimate the energy
of the ground state.

QUANTUM MECHANICS