Screen shot of free particle wavepacket.
The free particle wave packet program displays the time evolution of a free (V = 0 everywhere) initial Gaussian wave packet in position space. The default wave functions have expectation value of x = 0 and expectation value of p = 0, respectively. The Schrödinger equation determines the time evolution of this wave packet. Although the square of the area of the wave packet (total probability) remains constant, the wave packet spreads in position space as shown in this analytic solution. Why doesn't the wave packet change in momentum space?
David Griffiths Introduction to Quantum Mechanics 2ed Section 2.4.
The free particle wave packet JavaScript simulation was developed by Wolfgang Christian using the Easy Java/JavaScript Simulations (EjsS) modeling tool.