This project investigates the time evolution of a quantum wave packet under a linear gravitational potential using numerical methods implemented in Python.
The simulation explores the correspondence between quantum and classical motion by comparing the expectation value of the wave packet position with the classical trajectory predicted by Newtonian mechanics.
- Time-dependent Schrödinger equation
- Linear gravitational potential, V(x) = mgx
- Finite-difference discretization
- Crank-Nicolson numerical scheme
- Python
- NumPy
- Matplotlib
- Manim
The simulations demonstrate that the wave packet accelerates under gravity while simultaneously spreading due to quantum uncertainty.
The expectation value of position initially follows the classical trajectory, consistent with Ehrenfest's theorem, while deviations emerge over time because of wave packet dispersion.
- Python implementation (
.py) - Jupyter notebook (
.ipynb) - Simulation figures (
.png) - Manim animation (
.mp4)
Shahad AlDhafiri
Senior Undergraduate Computational Physics Student, Imam Abdulrahman Bin Faisal University