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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 # 12 due Thursday Oct 11 by 7pm A8, A9, A11, A14, 3.1, 3.2. Quantum mechanics. A friendly message from the TA to the students:

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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 # 12 due Thursday Oct 11 by 7pm • A8, A9, A11, A14, 3.1, 3.2

  3. Quantum mechanics A friendly message from the TA to the students: I have noticed in recent homeworks that more students quit to do entire problem(s). They are either short in time or overwhelmed by the length of the problems. It is understandable that this is an intense course, and the homework is time consuming. And as it is approaching the middle of the semester, all kinds of things are coming. But please be strong and do your best to learn. If you are really out of time, do as much as you can. Anyway, we don't want students to give up.

  4. Physical space • Linear transformation k k’ Matrix j’ • Transpose • Conjugate j Old basis New basis i i’ Quantum mechanics Review- Matrices Generalization (N-space) • Hermitian conjugate • Unit matrix • Inverse matrix • Unitary matrix Expressing same transformation T in different bases

  5. 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- algebra Pb A8 manipulate matrices, commutator transpose , Hermitian conjugate inverse matrix

  6. Wave function Vector Operators Linear transformation (matrix) Quantum mechanics Need for a formalism

  7. Operator acting on a wave vector: If T is Hermitian Expectation value/ Inner product Norm: Quantum mechanics Formalism N-dimensional space: basis

  8. Infinite- dimensional space Wave function are normalized: Hilbert space: functions f(x) such as Pb 3.1, 3.2 Quantum mechanics Hilbert space N-dimensional space Wave functions live in Hilbert space

  9. Norm Orthonormality Schwarz inequality Quantum mechanics Hilbert space Inner product

  10. Generalization of Determinate state: Standard deviation: For determinate state For a given operator Q: operator eigenstate eigenvalue Quantum mechanics Determinate states Stationary states – determinate energy

  11. Expectation value since For any f and g functions Observables are Hermitian operators Examples: Quantum mechanics Hermitian operators Observable - operator

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