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The term "harmonic oscillator" is used to describe any system with a "linear" restoring force that tends to return the system to an equilibrium state. There is both a classical harmonic oscillator and a quantum harmonic oscillator. Both are used as toy problems that describe many physical systems.

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Energy of the harmonic oscillator

We know the Hamiltonian of harmonic oscillator is $H={p^2\over{2m}} +{1\over 2} kx^2$. We then fix the value of the energy to the eigenvalues $E=(n+1/2) {h\omega\over{2π}}$ . But sometimes in the vi …
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