In what follows from the condition of electron diffraction from a crystal, it appears that low values of energy/momentum of the conduction electrons in metals should have a restriction.
In reference to my above mentioned question, it may also be noted that the electron in its ground state even in systems like liquid Helium-4 and Helium-3 occupy a state of non-zero energy. It exclusively occupy a large volume (Spherical cavity of about 38 Angstrom diameter) by displacing about 500 He atoms as a result of ts zero-point force on the neighbouring atoms). Similarly, a recent study of electron interaction with BEC by
Jonathan B. Balewski, et al [ Nature 502, 664–667 (2013) ]
also corroborates this observation. This study finds that the Rydberg electron is described by a wavefunction extending to a size of up to eight micrometres, comparable to the dimensions of the condensate. Evidently, a conduction electron in a conductor in its ground state is not expected to have zero energy. It has to have its lower bound. The Bragg reflection, the existence of electron bubble, and now the state of electron interacting with a BEC consistently prove this inference. This further concludes that the state of a conduction electron at T=0 is described closely by wave function similar to that of an electron trapped in a cavity of surrounding ions. Assuming that the electron is not able to displace the rigid positions of neighbouring ions significantly by its zero-point force, the lower bound of momentum should correspond to $\lambda = 2d$ which is consistent with the relation describing Bragg diffraction. Theories such as BCS theory of superconductivity dealing with conduction electrons should take care of this fact. This is one of the reasons that BCS type theories are inconsistent with certain physical realities of electrons in superconductors.
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