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Energy values in infinite potential well

  1. Apr 14, 2012 #1
    I was wondering why the spacing between energy values keep increasing for the infinite potential well?
     
  2. jcsd
  3. Apr 15, 2012 #2
    The energy equation for a particle inside an infinite square well is

    [itex]E_{n}[/itex] = [itex]\frac{\hbar^2 \pi^2 n^2}{8 m a^2}[/itex]

    So [itex]E_{n} \propto n^2 [/itex]

    So the relationship between energy and increasing n is non-linear.
     
  4. Apr 15, 2012 #3

    tom.stoer

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    The solution of the Schrödinger equation inside the square well is a plane wave identical to a free particle, but due to the boundary conditions only discrete levels n are allowed. The momentum p scales with n, i.e. p~n; the energy scales with p², so E=p²/2m~n².
     
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