Time Evolution of a Gaussian Wave Packet
- This computer visualization activity is designed to help upper-division undergraduate students understand the time evolution of a Gaussian wave packet.
- Students predicted the time dependence for a Gaussian distribution.
- The whole class discussion emphasizes that the solution to time-dependent Schrodinger's equation is a dispersive wave and focuses the difference between the dispersion relation for classical and quantum waves.
The free particle is one of the most fundamental quantum situations considered in advanced quantum courses and also one of the most complex of the archetypal examples. We discuss the Gaussian probability distribution with regards to transforming between position space and momentum space, and the connection between these representations of the wave function and the Heisenberg Uncertainty Principle. We emphasize the contrast between the non-dispersive wave equations considered in the classical context with the dispersive nature of solutions to the Schrödinger Equation.
This activity works particularly well when sequenced with other activities: