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 Sz, Sy, and S-. Since the electron has no kinetic energy, the energy eigenvalue corresponding to an eigenstate of the Hamiltonian is equal to mc^2, 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.

Name: consider the two spin eigenstates of the electron at rest you are given that the hamiltonian of this system commutes with the spin generators sz sy and s since the electron has no kinetic e 08103
Uploaded: 2023-08-23T13:57:29-08:00
Duration: 3 min 25 s
Channel: Isaac Huidobro
Description: consider the two spin eigenstates of the electron at rest you are given that the hamiltonian of this system commutes with the spin generators sz sy and s since the electron has no kinetic e 08103

          Consider the two spin eigenstates of the electron, at rest. You are given that the Hamiltonian of this system commutes with the spin generators Sz, Sy, and S-. Since the electron has no kinetic energy, the energy eigenvalue corresponding to an eigenstate of the Hamiltonian is equal to mc^2, 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.

Added by Tiffany C.

Chemistry: Structure and Properties

Nivaldo Tro 2nd Edition

Instant Answer

Solved by Expert Isaac Huidobro

08/23/2023

Step 1

This means that the total spin of the electron is conserved, and the energy eigenstates must be eigenstates of the total spin operator S^2. Show more…

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Consider the two spin eigenstates of the electron, at rest. You are given that the Hamiltonian of this system commutes with the spin generators Sz, Sy, and S-. Since the electron has no kinetic energy, the energy eigenvalue corresponding to an eigenstate of the Hamiltonian is equal to mc^2, 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.