Physics 424: Quantum Mechanics, Fall 2015 Reading/Homework Assignment 7 Due in Class Wednesday, 11/4/15 1 Reading • (Optional: Townsend Sec. 5.6 – Entanglement and Quantum Telepor- tation. Will not be covered in class or on tests but you might find interesting.) • Townsend Sec. 5.7 – The Density Operator • Townsend Sec. 5.8 – Summary • Townsend Sec. 6.1 – Position Eigenstates and the Wave Function • Townsend Sec. 6.2 – The Translation Operator • Townsend Sec. 6.3 – The Generator of Translations You don’t need the following section for these HW problems, but we will start discussing these topics in class: • Townsend Sec. 6.4 – The Momentum Operator in the Position Basis Problems to work out and turn in (70 pts total) 1. (10 pts) Show the following result, which we used in our discussion of Bells inequality: C ab = 4 ¯ h 2 h 0 , 0 | ˆ S a 1 ˆ S b 2 | 0 , 0 i = - cos θ ab . Here | 0 , 0 i is the singlet state of two spin-1/2 particles, ˆ S a 1 is the oper- ator for the component of spin 1 in the a direction, ˆ S b 2 is the operator for the component of spin 2 in the b direction, and θ ab is the angle between the a and b directions. Hint: Since the | 0 , 0 i state has no preferred direction, you are free (for example) to take the a direction to be z , and to take the
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