題組內容

15. (20 pts) Consider the spin state of a proton. Recall that the spin operators are5f5894ee026c1.jpgwhere i =5f58950a9249d.jpg. Suppose that a static external magnetic field is applied along the y direction, so that the hamiltonian is 5f58952a54d34.jpg where B is the magnetic field strength, and5f58954b1ef6d.jpg is a real constant. Denote the spin up state a and the spin down stateβ as5f58957369a39.jpg

(b) (A pts) Sol've the energy eigenvalues and their eigenvectors.