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Mean number of oscilatory quanta?

  1. Jan 18, 2017 #1
    A quantum mechanical oscillator with the Hamiltonian
    H1=p^2/2m +(m(w1)^2 x^2)/2

    is initially prepared in its ground state (zero number of oscillatory quanta). Then the
    Hamiltonian changes abruptly (almost instantly):
    H1→H2=p^2/2m +(m(w2)^2 x^2)/2
    What is the mean number of oscillatory quanta upon the transformation?

    My first question is what does oscillatory quanta exactly means?

    Attempt: Theory of quantum harmonic oscillator, the eigenstate formulas, the energy formulas. The only thing that is zero in ground state is n=0, so does it mean oscillatory quanta implies n quantum number.
  2. jcsd
  3. Jan 18, 2017 #2


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    You should have posted this in the homework forum, as you'll get a better response.

    Let me explain the question at least. The oscillator is in a known state (ground state for first Hamiltonian). The Hamiltonian changes, which means that the energy eigenstates change. Now you have effectively an initial value problem. You know the initial state/wave function, and this you need to express as a linear combination of your new eigenstates.

    I suspect the mean oscillatory quanta means the expected value of ##n## in your new system. Where ##n## represents the energy levels in your new system.
  4. Jan 18, 2017 #3
    Hi Perok,
    Sorry for posting it at wrong place.
    Do you mean that the my initial state is the ground state of the old Hamiltonian. Now since the Hamiltonian has changed, I need to express it(ground state from old Hamiltonian) as a combination of the eigenstates of new Hamiltonian?
  5. Jan 18, 2017 #4


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    Yes, that's what you have here.
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