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When dealing with Dirichlet boundary conditions, that is asking for the wavefunction to be exactly zero at the boundaries, it can be clearly seen that (0,0,0) is not a physical situation as it is not normalizable. (Wavefunction becomes just 0 then)
However when dealing with periodic boundary conditions, the basis is spanned by ##e^{i\vec{k}.\vec{r}}## where the only condition on ##\vec{k}## is that it has to correspond with ##L^{3}## cubic periodicity.
The problem now is that ##\vec{k}=0## does seem to give a non trivial solution with zero energy ##\Psi=constant## which is periodic and noralizable.
How do I interpret this werid 'constant' term in the general wavefunction part?
Sources:
Kittel eigth edition, p137
http://people.umass.edu/bvs/pbc.pdf
However when dealing with periodic boundary conditions, the basis is spanned by ##e^{i\vec{k}.\vec{r}}## where the only condition on ##\vec{k}## is that it has to correspond with ##L^{3}## cubic periodicity.
The problem now is that ##\vec{k}=0## does seem to give a non trivial solution with zero energy ##\Psi=constant## which is periodic and noralizable.
How do I interpret this werid 'constant' term in the general wavefunction part?
Sources:
Kittel eigth edition, p137
http://people.umass.edu/bvs/pbc.pdf