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Bose-Einstein-Condensate ground state energy E_0 = 0

  1. Jul 11, 2010 #1

    why is the ground state energy usually set to E_0 = 0 for a Bose gas?

    Normally one looks at a particle in a box, where the ground state energy should be different from 0.

    Here is the "particle in a box ground state energy" calculated in a Bose-Einstein contex:
    http://books.google.com/books?id=rI...A#v=onepage&q=bose gas "zero energy"&f=false"
    The author finds E_0 = 0

    In the follwoing calculation however, we find, as usual, that the ground state energy is not 0:

    How come, we can choose the ground state energy =0 for the Bose-Einstein-Condensate problem?

    Last edited by a moderator: Apr 25, 2017
  2. jcsd
  3. Jul 11, 2010 #2
    First off all, it's just a constant shift of the energy spectrum -- it's quite common to shift the Hamiltonian such that the lowest energy state has zero energy.

    But, the links you are providing do not treat the same problem: the first link has periodic boundary conditions, the wiki article does not. So a wavefunction which is constant everywhere appears in the first problem, but not in the second. A wavefunction which is constant, has zero derivatives and therefore zero kinetic energy.
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