08realH - P460 - real H atom 1 The Real Hydrogen Atom Solve...

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Unformatted text preview: P460 - real H atom 1 The Real Hydrogen Atom Solve SE and in first order get (independent of L): can use perturbation theory to determine: magnetic effects (spin-orbit and hyperfine e-A) relativistic corrections Also have Lamb shift due to electron self- interaction. Need QED (Dirac eq.) and depends on H wavefunction at r=0 (source of electric field). Very small and skip in this course (first calculated by Bethe using perturbation theory on train from Long Island to Ithaca. Bethe also in film Fat Man and Little Boy....) 2 6 . 13 n eV E n = P460 - real H atom 2 Spin-Orbit Interactions A non-zero orbital angular momentum L produces a magnetic field electron sees it. Its magnetic moment interacts giving energy shift in rest frame of electron, B field is (see book/ER): convert back to lab frame (Thomas precession due to non-inertial frame gives a factor of 2 Dirac eq gives directly). Energy depends on spin-orbit coupling B S g B F L dr r dV r emc B b s r r h r r r r = = = ) ( 1 1 2 = = E v B r v A B use c r r r r r r 2 1 L S dr dV r g emc E b s r r h = 1 2 1 2 P460 - real H atom 3 Spin-Orbit: Quantum Numbers The spin-orbit coupling (L*S) causes m l and m s to no longer be good quantum numbers spin-orbit interactions changes energy. In atomic physics, small perturbation, and can still use H spatial and spin wave function as very good starting point. Large effects in nuclear physics (and will see energy ordering very different due to couplings). So in atomic just need expectation value of additional interaction [ ] , , : ) ( 2 2 2 2 = = = + = H L HL L H L L ions eigenfunct also E H and r...
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08realH - P460 - real H atom 1 The Real Hydrogen Atom Solve...

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