Exact Numerical Solutions for the Stepped-Infinite-Square Well
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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.
Contributed by: M. Hanson (April 2011)
Open content licensed under CC BY-NC-SA
Snapshots
Details
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
Permanent Citation
"Exact Numerical Solutions for the Stepped-Infinite-Square Well"
http://demonstrations.wolfram.com/ExactNumericalSolutionsForTheSteppedInfiniteSquareWell/
Wolfram Demonstrations Project
Published: April 13 2011