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Hamiltonian of the Half Harmonic Oscillator

  1. May 2, 2015 #1
    Given the half harmonic potential:

    \begin{equation}V=\begin{cases}1/2\omega^2mx^2 & x > 0\\\infty & x < 0\end{cases}\end{equation}


    What will be the Hamiltonian of the half oscillator?


    I understand that for x>0 the Hamiltonian will be:

    \begin{equation}H=\frac{1}{2}\omega^2mx^2+\frac{P^2}{2m}\end{equation}

    But how do I find the Hamiltonian for the part when V = ∞?
     
  2. jcsd
  3. May 2, 2015 #2

    PeroK

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    The infinite potential simply constrains the particle to the region x > 0. The wave-equation for x < 0 must be 0. I can't see how you could define a Hamiltonian for this.
     
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