The Schrödinger Equation

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

\begin{displaymath}\bgroup\color{black}{-\hbar^2 \over 2m}\nabla^2\psi(\vec{x},t...
...vec{x},t)=i\hbar{\partial\psi(\vec{x},t)\over\partial t}\egroup\end{displaymath}

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


where (dropping the \bgroup\color{black}$(op)$\egroup label) \bgroup\color{black}$H={p^2\over 2m}+V(\vec{x})$\egroup 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