Wave functions must satisfy the
Schrödinger Equation
which is actually a wave equation.

We will use it to solve many problems in this course. In terms of operators, this can be written as

where (dropping the label) is the Hamiltonian operator. So the Schrödinger Equation is, in some sense, simply the statement (in operators) that the kinetic energy plus the potential energy equals the total energy.

Jim Branson 2013-04-22