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WOLFRAM|DEMONSTRATIONS PROJECT

Boundary Conditions for a Semi-Infinite Potential Well

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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.
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