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Quantized Solutions of the 1D Schrödinger Equation for a Harmonic Oscillator

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This illustrates the quantized solutions of the Schrödinger equation for the one-dimensional harmonic oscillator:

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As you vary the energy, the normalization and boundary conditions (for even or odd parity) are only satisfied at discrete energy values of the solution of the second-order ordinary differential equation. Boundary conditions are met when as and normalization is possible when exists.

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Contributed by: Jamie Williams (March 2011)
Open content licensed under CC BY-NC-SA

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