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When a particle in one dimension have discrete spectrum?

  1. Jul 10, 2011 #1
    What are the conditions for which it can be concluded that a system has discrete energy levels?
    For example a system in one dimension with the potential
    [itex]V(x)=b|x| [/itex]
    has only a discrete spectrum. How I can prove it?
    My book says moreover that the energy eigenvalues have to satisfy the condition
    [itex]\lmoustache_{x_1}^{x_2} dx \sqrt{2m[E- \lambda |x|]} = (n+1/2) \pi \hbar [/itex]
    why?

    thanks for help.
     
  2. jcsd
  3. Jul 10, 2011 #2
    In general, in cases where the minimum potential is bigger than the energy of the particle, you find that the general solution will be complex, and the energy takes a continuous form. on the other hand when the energy is bigger than the minimum potential, the solutions take discrete values as we have a bound particle.
     
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