Exact Numerical Solutions for the Stepped-Infinite-Square Well

This Demonstration shows the energy levels (light blue) and the wavefunctions (red and offset vertically by their energy) for the stepped-infinite-square well (dark blue) with step size selected using the slider. The left-hand tick marks correspond to the energy levels of a pure square well of width ; the energy level is identified by the square of its quantum number. The right-hand tick marks correspond to the energy levels of a pure square well of width , that is, the limit of an infinite step size.


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Snapshot 1: the step-free square well
Snapshot 2: at a step size 16 times the ground state energy there is a noticeable increase in wavefunction amplitude over the step for the third and fourth wavefunctions
Snapshot 3: for large step size the energy levels with higher values increase rapidly while those with lower values increase more slowly with step height
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