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- Use Dirac notation to calculate the separations in energy levels for a spin system consisting of two protons.Solve step by step please use THE ANGULAR MOMENTUM ADDITION THEOREMA hydrogen atom is located in an area where there is both a uniform magnetic field and a uniform electric field that are parallel to each other. a) write out the Hamiltonian of perturbation (ignore the spin of the electron). b) use perturbation theory in order to calculate the first order correction to the energy levels n=1,2 c) is there any degeneracy left? Compare with situations in which there is a magnetic field or only an electric field.
- How does this show that it's electron and proton spins are a eigenstate basis for this dipole interaction?Rewrite S₁ S₂ in terms of S², |S₁|², 5₂|² by using the identity |S² = |S₁ + S₂|² = |S₁|² + |5₂|² +25₁ · 5₂. Use this to show that the combined spin angular momentum basis 5² for the electron and proton spins is an eigenstate basis for this dipole interaction.There exists in nature a particle known as the muon. It is just a heavy electron with a mass mµ = 207me. It decaysin 10−6seconds. Suppose there exists a molecule analogous to H+2(two protons + 1 electron), but with the electronreplaced by a muon:(a) Find the equilibrium separation of the nuclei (R0) in such a molecule.(b) If a rotational state is excited, estimate the wavelength of the emitted radiation in the transition to the groundstate