Momentum Eigenstates

This Demonstration shows the motions of nonrelativistic one-dimensional momentum eigenfunctions. The time-dependent Schrödinger equation for a free particle in one dimension is given by . The eigenfunctions are , with a continuum of momentum eigenvalues , and energy eigenvalues . The energy eigenvalues are two-fold degenerate except for . The degeneracy corresponds to left-to-right motion when and right-to-left motion when .

For simplicity, we set . Plots are shown for the real and imaginary parts of as blue and purple sinusoidal curves, respectively. A three-dimensional representation is also shown.