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Physics 451

Physics 451. Quantum mechanics I Fall 2012. Oct 8, 2012 Karine Chesnel. Quantum mechanics. Announcements. Homework this week: HW # 11 due Tuesday Oct 9 by 7pm 2.38, 2.39, 2.41, A1, A2, A5, A7 HW # 12 due Thursday Oct 11 by 7pm A8, A9, A11, A14, 3.1, 3.2. Quantum mechanics.

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Physics 451

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  1. Physics 451 Quantum mechanics I Fall 2012 Oct 8, 2012 Karine Chesnel

  2. Quantum mechanics Announcements • Homework this week: • HW # 11due TuesdayOct 9 by 7pm • 2.38, 2.39, 2.41, A1, A2, A5, A7 • HW # 12 due Thursday Oct 11 by 7pm • A8, A9, A11, A14, 3.1, 3.2

  3. Quantum mechanics Test 1 Class average 78 / 100 Pb 1 17.6 / 20 Pb 2 13.5 / 20 Pb 3 16 / 20 Pb 4 14 / 20 Pb 5 16.8 / 20 Highest score: 95/100

  4. Quantum mechanics Need for a formalism

  5. Physical space k j i Quantum mechanics Vectors Generalization (N-space) • Addition • - commutative • - associative • Scalar multiplication • zero vector • linear combination • basis of vectors

  6. Generalization (N-space) “Inner product” Quantum mechanics Inner Product Physical space k B • Norm • Orthogonality • Orthonormal basis • Schwarz inequality q A j “Dot product” i

  7. Linear transformation Matrix • Transpose • Conjugate Quantum mechanics Matrices Physical space Generalization (N-space) k A’ • Sum • Product A’’ q j A • Hermitian conjugate • Transformations: • Multiplication • rotation • symmetric… • Unit matrix i • Inverse matrix • Unitary matrix

  8. Generalization (N-space) Old basis New basis Quantum mechanics Changing bases Physical space k k’ Expressing same transformation T in different bases j’ j Same determinant Same trace i i’

  9. Operator acting on a wave vector: Expectation value/ Inner product Norm: Quantum mechanics Formalism N-dimensional space: basis For Hermitian operators:

  10. Homework- Appendix Pb A1 manipulate vectors Check properties of vectorial space (sum, scalar multiplication, zero vector…) Pb A2Check vectorial properties for group of polynomial functions (sum, scalar multiplication, zero vector…) Pb A5 Proof of Schwarz inequality use Pb A14 Proof of triangular inequality use

  11. Pb A9 scalar matrix Pb A11 matrix product Pb A14 transformation: rotation by angle q, rotation by angle 180º reflection through a plane matrix orthogonal Homework- Appendix Pb A8 manipulate matrices, commutator transpose , Hermitian conjugate inverse matrix

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