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Understanding Spin and the Stern-Gerlach Experiment in Quantum Mechanics

This chapter explores fundamental concepts of spin in quantum mechanics, highlighting the Stern-Gerlach experiment's significance in demonstrating electron spin and intrinsic properties of particles such as fermions and bosons. It also discusses important principles like the Pauli exclusion principle that govern the behavior of these particles in multi-electron atoms, along with the historical developments in atomic theory, including the discovery of the electron and the nucleus. Prepare for upcoming quizzes and homework that delve deeper into these theories.

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Understanding Spin and the Stern-Gerlach Experiment in Quantum Mechanics

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  1. Spin and Atomic Physics Today HW 8, problem 7.38 Quiz 11.6 Topics in this chapter: The spin and the Stern-Gerlach experiment. Fermion, Boson and the Pauli exclusion principle. Multi-electron atoms and the Periodic Table. Characteristic X-rays.

  2. HW problem 7.38 Since it is an attractive central force and the angular momentum is given:    

  3. The Stern-Gerlach experiment in the history of QM The Balmer series 656 nm 410 nm 434 nm 486 nm 1885 Empirical formula in 1885: Electron discovered in by J.J. Thomson in 1897 1897 Rutherford discovered nucleus in 1909 1909 1913 Niels Bohr’s Hydrogen model in 1913 Stern-Gerlach experiment, electron spin in 1922 1922 The de Broglie wave (1924): The Schrödinger Equation (1926): 1924 1926

  4. The Stern-Gerlach experiment Interesting to read: http://scitation.aip.org/journals/doc/PHTOAD-ft/vol_56/iss_12/53_1.shtml

  5. The Stern-Gerlach experiment Classical Quantum observed WOW !

  6. The Stern-Gerlach experiment Quantum But: From: When ground state: But this was observed: WOW !!! What is this?

  7. Spin, an intrinsic property Spin: an intrinsic magnetic dipole moment of particles like electron, proton and photons. This dipole moment is related to an intrinsic angular momentum. The symbol is S, which is like L the orbital angular momentum. The corresponding quantum number is s. The spin magnetic dipole moment is Spin is an intrinsic property of a particle like mass and charge. Example 8.1 electron

  8. Fermions and Bosons Spin is an intrinsic property of a particle like mass and charge. Fermions Bosons (half-integral spin) (integral spin) Particle s Particle s Electron, e- ½ Pion, π0 0 Proton, p ½ Alpha 0 Neutron, n ½ Photon, γ1 Neutrino, ν½ Deuteron, d 1 Omega, Ω-½ Graviton 2

  9. The building blocks for our Universe Spin is an intrinsic property of a particle like mass and charge.

  10. The Pauli exclusion principle The Pauli exclusion principle (1924): No two indistinguishable fermions may occupy the same individual particle state. This principle applies only to fermions in In an atom, or an isolated system like a molecule. This principle does not apply to bosons.

  11. Review questions • What is the spin of a particle in CM and in QM? • Give one example in each the Pauli exclusion principle is applied.

  12. Preview for the next class (11/11) • Text to be read: • 8.4 and 8.5 • Questions: • Why we have H2 as hydrogen molecules while Ne as neon molecules? • What is the energy ordering of electron states in an atom with Z = 30? Can you fill the electrons for the element Zn if asked for?

  13. Homework 12, due by 11/13 Problems 8.28, 8.31 on page 339. Read section 8.2 and 8.3 one more time and see if you can answer questions in problem 8.7 on page 338.

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