Schrödinger equation

Separation of variables can also be a useful method for the time-independent Schrödinger equation. For example, depending on the symmetry of the problem, the Cartesian axes might be separated,

The general solutions of the Schrödinger equation for the particle in a box are

The Schrödinger equation for the hydrogen atom (or a hydrogen-like atom) is

The already ... mentioned psi-function.... is now the means for predicting probability of measurement results. In it is embodied the momentarily attained sum of theoretically based future expectation, somewhat as laid down in a catalog.