1 / 27

Modern physics and Quantum Mechanics Physical Systems, 8 Mar.2007 EJZ

Modern physics and Quantum Mechanics Physical Systems, 8 Mar.2007 EJZ. More angular momentum and H atom Compare to Bohr atom Applications: Bohr magneton, Zeeman effect Brief review of modern physics and QM Conferences next week Next quarter. Quantization of angular momentum.

lynton
Download Presentation

Modern physics and Quantum Mechanics Physical Systems, 8 Mar.2007 EJZ

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Modern physics and Quantum MechanicsPhysical Systems, 8 Mar.2007 EJZ • More angular momentum and H atom • Compare to Bohr atom • Applications: Bohr magneton, Zeeman effect • Brief review of modern physics and QM • Conferences next week • Next quarter

  2. Quantization of angular momentum Show that for ANY radial potential V(r) in the spherical Schrödinger equation, both the total angular momentum and the z-component are quantized. Last week we discussed the momentum operators…

  3. Spherical harmonics solve spherical Schrödinger equation for any V(r)

  4. Possible orientations of L and Lz (for l=2) Example 7.1 (p.300), #7.12, 7.14 (p.332)

  5. H-atom: quantization of energy for V= - kZe2/r Solve the radial part of the spherical Schrödinger equation (next quarter): Do these energy values look familiar?

  6. QM H-atom energy levels: degeneracy for states with different qn and same energy Selections rules for allowed transitions: l must change by one, since energy hops are mediated by a photon of spin-one. Dn = anything Dm can = ±1 or 0

  7. H-atom: wavefunctionsY(r,q,f) for V= - kZe2/r We already have the angular part of the wavefunctions for any radial potential in the spherical Schrödinger equation: We can solve (next quarter) for R(r) ~ Laguerre Polynomials

  8. H-atom wavefunctions ↔ electron probability distributions Discussion: compare Bohr model to Schrödinger model for H atom.

  9. A fourth quantum number: intrinsic spin If there are 2s+1 possible values of ms, and only 2 orientations of ms = z-component of s (Pauli), What values can s and ms have?

  10. Stern-Gerlach showed splitting due to spin, even when l=0 l = 1, m = 0, ±1 l = 0, m = ±1/2

  11. Spinning particles shift energies in B fields Cyclotron frequency: An electron moving with speed v perpendicular to an external magnetic field feels a Lorentz force: F=ma (solve for w=v/r) Solve for Bohr magneton…

  12. Magnetic moments shift energies in B fields

  13. Spin S and orbit L couple to total angular momentum J = L + S

  14. Spin-orbit coupling: spin of e- in magnetic field of pFine-structure splitting (e.g. 21-cm line) (Interaction of nuclear spin with electron spin (in an atom) → Hyper-fine splitting)

  15. Total J + external magnetic field → Zeeman effect

  16. Total J + external magnetic field → Zeeman effect

  17. Total J + external magnetic field → Zeeman effect

  18. History of Light quantization • Stefan-Boltzmann blackbody had UV catastrophe • Planck quantized light, and solved blackbody problem • Einstein used Planck’s quanta to explain photoelectric effect • Compton effect demonstrated quantization of light • Corrollary: deBroglie’s matter waves, discovered by Davisson & Germer hc/l = Kmax + F

  19. History of atomic models: • Thomson discovered electron, invented plum-pudding model • Rutherford observed nuclear scattering, invented orbital atom • Bohr quantized angular momentum, for better H atom model. • Bohr model explained observed H spectra, derived En = E/n2 and phenomenological Rydberg constant • Quantum numbers n, l, ml (Zeeman effect) • Solution to Schrodinger equation showed that En = E/l(l+1) • Pauli proposed spin (ms=1/2), and Dirac derived it

  20. deBroglie’s matter waves  Bohr’s angular momentum quantization Compton Effect

  21. Quantum wells

More Related