24. Electron-positron pairs are emitted in a decay process (moving in opposite directions) in a spin state |0 ,0 i spin = | s, m i of zero total spin angular momentum ~ S = ~ S 1 + ~ S 2 . (a) What is the mean value that will be obtained in a measurement performed on an ensemble of such electron-positron pairs of the operator S 1 z S 2 z ? Is the value the same as that which one would obtain by independently measuring the values of S 1 z and of S 2 z and forming the product of the mean values of each? Explain. (b) What is the mean value that will be obtained in a measurement performed on an ensemble of such electron-positron pairs of the operator S 1 x S 2 x ? (Feel free to use any appropriate symmetry argument.) (c) If the operator ~ S 1 · ~ S 2 is measured on this state, what values can be obtained, and with what probability will they occur? 25. Consider two identical particles that are in states of total angular momentum j in the direct product space S ( j 1 ,j 2 )= S ( j 1 ) × S ( j
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This note was uploaded on 12/19/2010 for the course PHYSICS ph 463 taught by Professor Paule. during the Fall '10 term at Missouri S&T.