Solving the Schr�dinger Equation with a Hand-Held Calculator

Abstract

A rather simple method of numerical integration, the Euler method, is applied to the one-dimensional Schrodinger equation for a paticle bound to a finite square well, a case which is exactly solvable by analytical methods. Insight is gained into the dominant role played by the boundary conditions in the solution of eigenvalue equations. Comparison is made with the exact soution of the algebraic methods, which leads to the discussion of improving the method, or switching to more sophisticated procedures. Though the results presented came from calculations performed on a nonprogrammmable calculator, programmable ones could be used. The same treatmnent can be applied to more complex potentials, for example two-and three-dimensional ones. The beauty of the method is that the solution seems to come from the calculating fingers rather than from an abstract equation. Emphasis is on the physics rather than on the calculator.