(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, m ₑ c ² ? Express your answer in terms of the parameter λ _ C = h / m ₑ c, the ‘Compton wavelength’ of the electron. (b) Repeat Exercise (a) for a general particle of mass m in a cubic box.
a) L/λ_C = π/2
b) L/λ_C = √3
c) L/λ_C = π
d) L/λ_C = 2π