• Question: Whats the quantum harmonic oscillator including its energy spectrum?

    Asked by 06chrste to James, Marcus, Martin, Rob, Suzanne on 19 Mar 2012.
    • Photo: Martin Zaltz Austwick

      Martin Zaltz Austwick answered on 19 Mar 2012:

      It’s a quantum mechanical version of a harmonic oscillator, which is surprisingly common in nature. A mass (weight) on the end of a spring is one, for example, and they come up in different ways in atomic physics and electronics, so physicists like them a lot. (The energy eigenvalue of the nth eigenstate of a QHO is (n+(1/2))hf, but that’s not very interesting unless you follow all the maths through!)

    • Photo: Suzanne McEndoo

      Suzanne McEndoo answered on 19 Mar 2012:

      Yeah, we do love the quantum harmonic oscillator. It’s particularly interesting because a lot of big things just look like a quantum harmonic oscillator (I’m going to start writing QHO too, save my fingers) when we get small enough for quantum physics. When we talk about trapping atoms, the tip of the trap where the atom is is a QHO, so when we want to talk about the energy spectrum or wave functions of the atom, we can use the QHO ones that we’ve already worked out.

      The fun thing about the QHO is that the energy of the nth level, as Martin says, is (n+1/2)hf, so the lowest (the 0th) level, which we call the ground state, has an energy of 1/2 hf. This means that in a QHO you can never have zero energy!

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