Practice final This test is too long for the 75 minutes you have today; it would

Question

Practice final This test is too long for the 75 minutes you have today; it would be appropriate for the final. I strongly encourage you to at least try each problem today, with your real tools, "cheat sheet", etc 0.1 Quick problem 1 Two particles of spin S1 and S2 (neither equal to zero) sit in a magnetic field B They have the Hamiltonian What are the good quantum numbers of this system? 0.2 Quick problem 2 Two particles of spin S1 and S2 (neither equal to zero) are coupled together. They have the Hamil- tonian What are the good quantum numbers of this system? 0.3 Quick problem 3 Suppose you have three particles, one in state , one in ob, and one in ore. If the particles were distinguishable, we could construct an allowed composite wavefunctionai vo; Vb) Construct an allowed wave function for the three particles if they are 1. fermions 2. bosons 0.4 Quick problem 4 I have a spin 1/2 particle in a magnetic field B. The Hamiltonian is: I measure S and get a result of t/2. 1. If I immediatel ly measure Sa, what answers might I get, and with what probabilities? 2. If I wait a long time an measure S;, what answers might I get, and with what probabilities? 0.5 Quick problem 5 You have two spin 1/2 particles, a proton and an electron. The states are lS example, the state IT) has the proton spin up (m, h/2)and the electron spin d This is just what we usually do. -protonS-electron). For own (m,-h/2) Which of the following states are entangled: 1. Itt) 2. It)

Explanation / Answer

5) For entangled states, the wave function cannot separated as individual wave functions. In the given five options, 1 and 2 can be separated where as 3, 4, and 5 cannot be separated. So the states 3, 4, and 5 are entangled.

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