Question about the continuous beta-spectrum

[Jack_G]

The last days I have been thinking about the following question.

How does standard QM explain the continuous spectrum in beta-decay? Why can the created electrons (and, hence, also the neutrinos) in beta-decay acquire any possible energy within a certain range as long as their sum conserves the energy? I would have suspected that the new electrons can be created with an energy from a limited set of possible energies, with the neutrinos acquiring the matching energy from a set with the same cardinality.

 

[muppet]

To a first approximation, the electron and the anti-neutrino are free particles, so their energies are eigenstates of the laplacian, proportional to k^2. If your beta decay occurred inside a "box" whose characteristic dimensions were comparable to the de Broglie wavelength of the particles, then you'd have a noticeably finite spacing of energy levels, but the universe is big enough for any such spacing to be completely negligible.