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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 (spinorbit and hyperfine eA) 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 SpinOrbit Interactions • A nonzero 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 noninertial frame gives a factor of 2 – Dirac eq gives directly). Energy depends on spinorbit coupling B S g B F L dr r dV r emc B b s r r h r r r r • − = • − = Δ = μ μ ) ( 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 • = Δ 1 2 1 2 μ P460  real H atom 3 SpinOrbit: Quantum Numbers • The spinorbit coupling (L*S) causes m l and m s to no longer be “good” quantum numbers • spinorbit 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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This note was uploaded on 10/02/2009 for the course PHYS 460 taught by Professor Johnson,c during the Spring '08 term at Northern Illinois University.
 Spring '08
 Johnson,C
 Quantum Physics

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