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Quantum II (PHYS 4410)

Lecture 3. Spin ½ continued. Quantum II (PHYS 4410). Prof. Chuck Rogers : Charles.Rogers@colorado.edu 303-492-4476 Office hours : MF 4-4:45P after class, start here and then migrate to Duane F-631 Homework sessions : Thursdays 4-6PM Duane D-142

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Quantum II (PHYS 4410)

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  1. Lecture 3 Spin ½ continued. Quantum II (PHYS 4410) Prof. Chuck Rogers: Charles.Rogers@colorado.edu 303-492-4476 Office hours: MF 4-4:45P after class, start here and then migrate to Duane F-631 Homework sessions: Thursdays 4-6PM Duane D-142 Website: http://www.colorado.edu/physics/phys4410

  2. Consider three functions f(x) , g(y), and h(z) which obey the equation:f(x) + g(y) + h(z) = C = constant. How many of the functions must be constant? If H is a sum, Y is a product. A) f, g, and h must all be constants. B) One of f, g, and h, must be a constant. C) Two of f, g, and h must be constants. 81

  3. You have two spins, so you create a new hermitian operator: Therefore, you expect that the eigen vectors of this hermitian operator are: • A sum of the electron and proton eigen vectors. • A product of the ele. and prot. Eigen vectors. • Something else

  4. You have two spin ½ objects and consider the sum of their z-components of spin: What is the maximum value you expect for the quantum number mtotal • ½ • 0 • 1 • 2 • Something else.

  5. In spin space, the basis states (eigenstates of S2, Sz ) are orthogonal: Are the following matrix elements zero or non-zero? • Both are zero • B) Neither are zero • C) The first is zero; second is non-zero • D) The first is non-zero; second is zero 149

  6. TRUE (A) or FALSE (B): … is a hermitian operator.

  7. The 2x2 matrix representation of the s =1/2 operator for Sy is: Syis a hermitian operator. The possible results of a measurement of Syare: +/- 1 +/- i +/- Impossible to know due to the Uncertainty Principle

  8. A spin ½ particle in the spin state A measurement of Sz is made. What is the probability that the value of Sz will be ħ/2? A) B) C) D) E) None of these 150

  9. A spin ½ particle is in a spin state (a “spinor”) A measurement of Sz is made. What is the probability that the value of Sz will be -ħ/2? A) B) C) D) E) None of these 150

  10. A large number of spin ½ particles are in: Many measurements of Sz are made. What is the average outcome of those measurements? A) B) C) D) E) None of these

  11. A spin ½ particle is in the +ħ/2 eigenstate of (i.e, it has a definite value for the x-component of spin, +ħ/2) Suppose we immediately measure Sz. What is the probability that this measurement will yield Sz= +ħ/2? • Zero B) 25% C) 50% • D) 100% E) other/Impossible to say 154

  12. Suppose a spin ½ particle is in the spin state Suppose we measure Sx and then immediately measure Sz. What is the probability that the second measurement (Sz) will leave the particle in the Sz = down state • Zero • Non-zero 154

  13. Consider two possible states for a spin ½ particle: Is there any physical (measurable) difference between these two states? • No, they are indistinguishable(phases, like -1, don’t matter in QM) • B) Yes, they are easily distinguishable

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