Answered: electron has no kinetic energy, the…

electron has no kinetic energy, the energy eigenvalue corresponding to an eigenstate of the Hamiltonian is equal to me2, where m is the rest mass of the electron in that state.

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Question

Consider the two spin eigenstates of the electron, at rest. You are given that the Hamiltonian of this system commutes with the spin generators Sr. Sy and S₂. Since the electron has no kinetic energy, the energy eigenvalue corresponding to an eigenstate of the Hamiltonian is equal to me2, where m is the rest mass of the electron in that state.

(a) Show that the electron with spin-up has the same rest mass as the electron with spin down

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