Adjusting the Zero Point Energy

As students of quantum mechanics should know, the solution to the quantum harmonic oscillator Hamiltonian gives an elegant result:

En=(n+12)ωE_n = (n+\frac{1}{2})\hbar\omega

There's a constant term in the energy when nn is zero. This is called the Zero Point Energy.

A student proposes that we get rid of this ridiculous term by simply redefining the Hamiltonian as


After all, we do this all the time with gravity problems simply by adjusting the reference point.

Is this student successful in removing this offset?


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