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Homework Help: Quantum harmonic oscl. half space potential

  1. Oct 25, 2004 #1
    I'm trying to figure out what happens to the energy eigenstates when the quantum harmonic oscillator potential is over [0..infinity] rather then
    [-infinity..infinity]. Originaly its hw(n +1/2)...

    Thanks
     
  2. jcsd
  3. Oct 26, 2004 #2

    Tom Mattson

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    The half space SHO is what you get when you superpose the SHO with an infinite wall. Since a wavefunction cannot penetrate an infinite wall, you have to have a node there. So of all the regular SHO solutions, only the ones with a node at the origin survive. Their corresponding energies are the only allowed energies.
     
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