Quantum Mechanics
Motion in potential: Particle in a box

Time-independent Schrödinger equation

An equation of the type Time-independent Schr&oumldinger equation is called an eigenvalue equation: A solution Phi (r) is an eigenfunction of the Hamiltonian H and E is the corresponding eigenvalue. The form of the Hamiltonian H and the boundary conditions imposed on Phi (r) determine the solutions of the eigenvalue equation.