Principles of Quantum Mechanics · Problem 5.3.4

The Classical Limit — R. Shankar

Physics — Quantum Mechanics · probability-current-superposition

Problem

Consider

\psi = A\, e^{ipx/\hbar} + B\, e^{-ipx/\hbar}

in one dimension. Show that

j = (|A|^2 - |B|^2)p/m

. The absence of cross terms between the right- and left-moving pieces in

\psi

allows us to associate the two parts of

j

with corresponding parts of

\psi