Question

PLEASE COMPLETE B) and stay tuned for my following 2 questions where I will ask part c) and d). Part a) has already been posted.

The lowest energy state of a hydrogen-like atom has total angular momentum J-1/2 (from the l-O orbital angular momentum and the electron spin s 1/2). Furthermore, the nucleus also has a spin, conventionally labeled I (for hydrogen, this is the proton spin, 1 1/2). This spin leads to an additional degeneracy. For example, in the original hydrogen atom solution not counting fine structure and other perturbations - there would be a four-fold degeneracy in the ground state, since m, (eigenvalue of the electron angular momentum operator J) and m (eigenvalue of the nuclear angular momentum operator Iz) can each take two different values. 1. In this problem, we will analyze a fictitious hydrotron atom. Hydrotron is exactly like hydrogen, except its nuclear spin is 1 3/2. b. The hyperfine interaction is expected to partially lift this degeneracy (shifting previously degenerate states by differing energies). Calculate the first order energy shifts from this Hamiltonian: Hhyperfine AI The convention for labeling the total angular momentum of the atom is to define F I +J (where bold letters indicate vector operators). The notation Im, m,) is used to denote the joint eigenstates of I, and J with eigenvalues hm and hm,, while lf,my) is used to denote the joint eigenstates of F2 and F with eigenvalues h2ff + 1) and hmf, respectively Which states are shifted by what energies?

Answer 1

17) 쮜 니 니 쒸부 8 15-3 2. 互肚,