Operators in Position Space

To find operators for physical variables in position space, we will look at wave functions with definite momentum. Our state of definite momentum \bgroup\color{black}$p_0$\egroup (and definite energy \bgroup\color{black}$E_0$\egroup) is

\begin{displaymath}\bgroup\color{black}u_{p0}(x,t)={1\over\sqrt{2\pi\hbar}}e^{i(p_0x-E_0t)/\hbar}.\egroup\end{displaymath}

We can build any other state from superpositions of these states using the Fourier Transform.

\begin{displaymath}\bgroup\color{black}\psi(x,t)=\int\limits_{-\infty}^{\infty}\phi(p) u_p(x,t) dp\egroup\end{displaymath}



Subsections

Jim Branson 2013-04-22