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Hello everyone.
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In this problem, we're asked to use symmetry arguments and looking at the good debate functions of the simple harmonic oscillator to derive what are the possible energy levels for the following potential.
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So the potential is infinity.
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So it's infinite everywhere where x is smaller than or equal to zero, and it is of the form of the harmonic oscillator at x positive.
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So this potential is known as the half harmonic oscillator.
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So half harmonic oscillator.
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Okay, so that's the potential that we're dealing with.
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This is what it looks like.
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And so there are two regions, right? one where the potential is infinite and one where it is of the form of the harmonic oscillator.
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Now, where the potential is infinite, the wave function vanishes.
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So psi, the wave function in the first region, is zero.
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Whereas in the second region, we have the harmonic oscillator potential, and so the solutions are the solutions to the harmonic oscillator problem...