# Bose-Einstein-Condensate ground state energy E_0 = 0

1. Jul 11, 2010

### Derivator

Hi,

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:
The author finds E_0 = 0

In the follwoing calculation however, we find, as usual, that the ground state energy is not 0:
http://en.wikipedia.org/wiki/Particles_in_a_box#Energy_levels"

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

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derivator

Last edited by a moderator: Apr 25, 2017
2. Jul 11, 2010

### xepma

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.