Thermodynamics, Statistical Physics, and Quantum Mechanics

QUANTUM MECHANICS

5.11 Square Well (MIT)

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a) The most general solution is

We evaluate the coefficients by using the initial condition at = 0:

The term cos iseither 1, 0, or –1, depending on the value of The

answer to (a) is to use the above expression for in (S.5.11.3). The answer

to part (b) is that the probability of being in the eigenstate is

The answer to part (c) is that the average value of the energy is

This latter series does not converge. It takes an infinite amount of energy

to form the initial wave function.

5.12 Given the Eigenfunction (Boston, MIT)

We evaluate the second derivative of the eigenfunction, which gives the
kinetic energy: