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Using the built-in differential equation solvers and graphical
capabilities
of Mathcad, students can visualize the wavefunctions of the
particle-in-a-box potential. By applying the mathematical requirements
of the wavefunction, the particle in a box is seen to have quantized
energies. By plotting possible solutions, students are able to
visualize the consequences of requiring the wavefunction to be
continuous. Also, the step potential and barrier potential can be
examined, thus allowing students to see how requiring the wavefunction
to be finite results in the quantum mechanical phenomenon of
tunneling. The instructor notes include Mathcad graphics
illustrating some of the peculiar features of the simple particle in a
box, the step potential, and the double-well barrier potential.
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| Figure 1. Mathcad plot (in arbitrary units) of wavefunction
for quantum number n = 3 showing tunneling for the step potential V(x)
= 0 at 0 < x < 2 and V(x) = 20 at 2 ≤ x < 4. Z0 is the vector containing the values of x and Z1 is the vector containing the values of the wavefunction at x. |
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