Enriching Elementary Quantum Mechanics with the Computer: Self-Consistent Field Problems in One Dimension

The use of a computer in undergraduate physics courses opens the door to a large number of instructive problems which were once precluded due to the necessity of numerical analysis. One such example for elementary quantum mechanics is the problem of a bound system of more than two particles which may be solved by the method of the self-consistent field (SCF). This paper discusses one-dimensional systems of particles whose solutions are obtained by the SCF method using the Hartree approximation. The procedure is shown to be a simple extension of programs which many undergraduates already use to obtain computer solutions of the Schrödinger equation in one dimention. Calculations for these systems serve as a useful introduction to iterative techniques, and the results provide the student with insight into the nature of atomic calculations for multi-electron atoms.