Momentum Eigenstates

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

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.


Contributed by: S. M. Blinder (February 2012)
Open content licensed under CC BY-NC-SA




[1] S. M. Blinder, Introduction to Quantum Mechanics, Amsterdam: Elsevier, 2004 pp. 31–32.

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.