Linear Operators

Linear operators $\bgroup\color{black}$L$\egroup$ satisfy the equation

$\bgroup\color{black}$\displaystyle L(a\psi+b\phi)=aL\psi+bL\phi$\egroup$

where $\bgroup\color{black}$a$\egroup$ and $\bgroup\color{black}$b$\egroup$ are arbitrary constants and $\bgroup\color{black}$\psi$\egroup$ and $\bgroup\color{black}$\phi$\egroup$ are arbitrary wave-functions. A multiplicative constant is a simple linear operator. Differential operators clearly are linear also.

An example of a non-linear operator (which we will not use) is $\bgroup\color{black}$N$\egroup$ which has the property

$\begin{displaymath}\bgroup\color{black}N\psi=\psi^2.\egroup\end{displaymath}$

Jim Branson 2013-04-22