No it doesn't. The conduction band of a conductor is derived using quantum theory, and that's continuous. The energy and momentum of a free particle can be anything when you solve the Schrodinger equation. There's no "quantization" there.
I would like to know how to calculate the ##[\hat{H}, \hat{P}]## for a particle in a 1D box? At the first glance it seems that they commute but they don't get diagonalized in identical basis. How to calculate this commutation?
I don't know why the electrons in atoms are considered in the orbitals while they could be in sates which are superpositions of these orbitals? If electrons are in the superposition of these orbitals their energy expectation value is also constant, and the atom seems to be stable!