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Quantum Mechanics: Angular Momentum and Eigenstates

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This course covers the principles of quantum mechanics, focusing on angular momentum and eigenstates. Topics include spherical coordinates, the Schrödinger equation, quantum numbers, spin, and the Pauli matrices.

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Quantum Mechanics: Angular Momentum and Eigenstates

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  1. Physics 451 Quantum mechanics I Fall 2012 Nov 12, 2012 Karine Chesnel

  2. Quantum mechanics Announcements • Homework this week: • HW #19 Tuesday Nov 13 • Pb 4.14, 4.15, 4.16, 4.17 • HW #20 Thursday Nov 15 • Pb 4.18, 4.19, 4.21, 4.22 Test 3 Review Monday Nov 19- 20 Sign for practice test

  3. Top Value =+l Eigenstates Bottom Value = -l Quantum mechanics The angular momentum Ladder operator

  4. Pb 4.18 Quantum mechanics The angular momentum

  5. z r y x Quantum mechanics The angular momentum In spherical coordinates

  6. z r y x Quantum mechanics The angular momentum In spherical coordinates Pb 4.21, 4.22

  7. z r y x and Quantum mechanics The angular momentum eigenvectors were the two angular equations for the spherical harmonics! Spherical harmonics are the eigenfunctions

  8. z r y x Quantum mechanics The angular momentum and Schrödinger equation 3 quantum numbers (n,l,m) • Principal quantum number n: integer • Azimutal and magnetic quantum numbers (l,m) • can also be half-integers.

  9. Quantum mechanics Quiz 26 For a given n value, how many eigenstates can we find for the operator ? • A. 0 • B. • D. • E.

  10. orbital spin Quantum mechanics The Spin Types of angular momentum

  11. Representation of Quantum mechanics Agular moment in the atom • Orbital moment (l) • Spin moment (s)

  12. Fermions: (S half-integer) S=1/2 Leptons: electrons,… Quarks: u,b,c,s,t,b • Bosons: (S integer) Photon S=1 Quantum mechanics Spin in elementary particles Each elementary particle is characterized by an immutable spin S Proton, neutron Mesons

  13. Quantum mechanics The spin

  14. Quantum mechanics The spin

  15. Spin up Spin down Quantum mechanics The spin 1/2 The “spinor”

  16. Quantum mechanics Pauli matrices Pb 4.29

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