You have the excited states of He with the configuration 2p1 3p1, in which the two electronshave different principal quantum numbers. The electrons are coupled by a Russell-Saundersspin-orbit coupling term in the Hamiltonian, § ' Ľ · S, where § ' is a positive constant.1. What are the possible term symbols for the energy eigenstate states associated with thisHe configuration? Show your work. If you had a low Z (atomic number) atom, do you generally expect singlet spin stateterms to have lower or higher energy than triplet spin state terms? On what physicalgrounds do you rest your argument?3.

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There is an electron, in a 1-d, infinitely deep square potential well with a width of d. If it is in ground state, 1. Draw the electron's wavefunction. Show the position of the walls of the potential well. 2. Explain how the probability distribution for detecting the electron at a given position differs from the wavefunction.
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Exercise b. Hard spin glasses.Physicists use a model called an Ising spin glass to study magnetic materials. We havea graph G = (V, E) and a function J : E → Z, where J(u, v) is the interaction strengthof edge {u, v} ∈ E. A state is a function s : V → {−1, +1}.1 The energy of a states is H(s) = −P{u,v}∈EJ(u, v) · s(u) · s(v).2 An edge {u, v} is called ferromagnetic ifJ(u, v) > 0, and antiferromagnetic if J(u, v) < 0. Ferromagnetic edges “pressure” uand v to be the same spin, and antiferromagnetic edges “pressure” them to be different.We wish to find the ground state, i.e., values of s(u) for each u ∈ V that minimize theenergy. Phrased as a decision problem, we ask whether a state exists below a certainenergy threshold:Spin-GlassInput: a graph G = (V, E), interaction strengths J : E → Z, and a threshold hˆ ∈ ZQuestion: is there a state s : V → {−1, +1} with H(s) ≤ hˆ?Show that Spin-Glass is NP-complete.1Each s(u) is called the spin of u; if u is a magnetic domain, think of s(u) as…