Variational Principle for Quantum Particle in a Box

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 variational principle applied to the quantum particle-in-a-box problem. The Hamiltonian describing the particle is , and the eigenfunctions and eigenvalues are given by and , respectively. If is a trial wavefunction that depends on the variational parameter , then minimizing the energy functional with respect to leads to an estimate for the energy. In this example, the values of that minimize are and , . The left panel shows the energy estimate and the three lowest eigenenergies, where the red are located at the , and the right graphic shows the normalized trial wavefunction for the ground and second excited states, which are the lowest even functions with respect to the central point.

Contributed by: Porscha McRobbie and Eitan Geva (March 2011)
Open content licensed under CC BY-NC-SA




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.