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Quantum Mechanics: Angular Momentum and Eigenstates

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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