Boundary Conditions for a Semi-Infinite Potential Well

energy

This Demonstration shows the solutions to the time-independent Schrödinger equation, treating energy as a continuous parameter. Once appropriate boundary conditions are applied, the energy levels become quantized and the corresponding eigenfunction and its first derivative are continuous across the

x=1

boundary. The left and right panels show the wavefunction and corresponding energy, respectively. If the energy is equal to one of its eigenvalues, the wavefunction is smooth across the boundary; otherwise it develops a kink.