Solution for a Single Free Particle
Claimed by Carlos M. Silva (Spring 2022)
The Schrödinger Equation is a linear partial differential equation that governs the wave function of a quantum mechanical system[1]. Similar to Newton's Laws, the Schrödinger Equation is an equation of motion, meaning that it's capable of describing the time-evolution of a position analog of a system.
The free particle is the name given to the system consisting of a single particle subject to a null or constant potential everywhere in space. It's the simplest system to which the Schrödinger Equation has a solution with physical meaning.
Although the free-particle solution does not have ample practical use in the field of Physics, the methods and conclusions that come from the solution of this system are of great use in a plethora of other quantum systems.
References
- ↑ Griffiths, David J. (2004). Introduction to Quantum Mechanics (2nd ed.). Prentice Hall. ISBN 978-0-13-111892-8.