(a) An electron is confined to a square well of length L. What would be the length of the box such that the zero-point energy of the electron is equal to its rest mass energy, m₄ c² ? Express your answer in terms of the parameter λ_c=h / m₄ c, the 'Compton wavelength' of the electron. (b) Repeat for the case of a cubic box of side L.
a) L/λ_c = π/2
b) L/λ_c = √3
c) L/λ_c = π
d) L/λ_c = 2π