This differential equation is in precisely the same form as the key equation for quantum mechanics, the Schrödinger wave equation, and in fact we will use it to (sort of kind of) derive the Schrödinger wave equation. The quantum treatment of any chemical problem begins by setting up appropriate boundary conditions for this wave equation. The solutions ψ(x) of the wave equation are known as wavefunctions: they contain all the information we can hope to learn about the problem. That information can be retrieved by performing certain mathematical operations on the wavefunction. These three steps:
- setting up the wave equation;
- solving it to obtain the wavefunction;
- using the wavefunction to obtain energies, momenta, etc...
are standard procedures for any quantum mechanical problem.
