By John David Jackson
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Extra info for Mathematics for Quantum Mechanics: An Introductory Survey of Operators, Eigenvalues, and Linear Vector Spaces
It slides down and then up the other side (there is no friction here). If you did not pull it very high up, then it won’t get over the hump in the middle before stopping and sliding down and then back up the right side again. However, if you took it high enough (higher than the hump’s top), then it would still have enough kinetic energy at the midpoint to go over the top, slide down to the left, up the side, back down, up over the hump, and so on. 1 A double-well potential energy curve. If a particle starts out in the right well, could it get to the left?
Now suppose our particles are in this singlet state, and the positron is moving at a fast speed to the left, and the electron rapidly to the right. We have two experimenters, Alice and Bob. (Physicists like to give names to the typical workers in the lab. Instead of calling them A and B, we introduce Alice and Bob. ) Alice is in position to measure the spin of the positron when it gets to her; Bob plans to measure the spin of the electron that is traveling toward him. If Alice finds the positron has up spin along z, then Bob must measure a down spin along z.
5, we find that the turning points become more favored. This corresponds to the usual feature of quantum mechanics that we approach classical behavior when the quantum energy states become large. This is an example of the correspondence principle of Niels Bohr: high quantum energy corresponds to classical behavior. In Chaps. 4 and 5 we use quantum oscillators to illustrate the concepts of superposition and entanglement. 4 Superposition The greater the ambiguity, the greater the pleasure. M ILAN K UNDERA Waves add up.
Mathematics for Quantum Mechanics: An Introductory Survey of Operators, Eigenvalues, and Linear Vector Spaces by John David Jackson