The half-harmonic quantum oscillator

Simulation

Challenges

Wave function ψ1

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Potential energy V(x)

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Harmonic oscillator: V(x) = 1/2 m ω2 x2 for all x

Half-harmonic oscillator: V(x) = 1/2 m ω2 x2 for x>0; V = ∞ for x ≤ 0

Quantum number n = 1

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The text on start-up appears here.

Main controls

Quantum number n = 1

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Angular frequency ω

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ψ(x) graph

|ψ(x)|2 graph

E0 = ℏω(0 + 1/2) = 1/2 ℏω