Question

Estimating minimum energy of a confined particle using uncertainty principle

Answer 1

The form of your book's value ℏ22ma2ℏ22ma2 makes it clear that that is a fully classical (non-relativistic) limit (p22mp22m , right?), while yours is a fully relativistic one (after all E,p≫meE,p≫me ).The argument about the nuclear confinement is simply that both the gravitational and electromagnetic potentials on the electron due to the nucleus are many orders of magnitude smaller than 40 MeV (the weak nuclear force too, but you may not know how to compute this), and the electron is not affected by the strong nuclear force.