PHYSICS 002C Lecture 25

PHYSICS 002C Lecture 25 - PHYSICS 002C Lecture 25 May 29,...

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PHYSICS 002C Lecture 25 May 29, 2009 Serway and Jewett Chapter 29 – Atomic Physics Chap 29 Binding of atoms and identical particles For some unknown reason us creatures have something called consciousness, which means we are autonomous and we know it. But what seems most strange is that one of them is me! So it is hard to grasp one of Dalton’s laws – all atoms of a given [isotope] are the same. Maybe, you might say, two atoms are like identical twins – they are very similar except they have different histories that make them a little bit different. OK, let’s try an experiment – we will keep track of our pet atom to make sure it doesn’t get lost. Following the work of the famous physicist Steve Chu [Nobel Prize 1997] one may hold a single atom trapped in a focused laser beam, just off resonance. Your pet Na atom is now distinct from mine because they are in separate traps. But suppose a wild atom of the same species zooms past and happens to come near my pet. If there is a small interaction between the atoms, say of size  , due to the bumping into each other or attracting each other, then after a time E h t / you are not going to be able to tell which is wild and which is tame. So you can keep track of individual atoms, but only if they are not allowed to interact too much. As far as having a different history like a human twin, there are not enough quantum numbers inside an atom to carry around a complicated history. If the atoms are in the same state, namely all their internal quantum numbers are the same, they have no history except to the extent that you can follow their trajectories. Chap 29.5 The Pauli exclusion principle Two identical half-integral spin objects cannot be in the same state. Q: What does it mean to have 2 objects that are identical? (a) if you scatter them off a wall they do not stick; (b) if you switch them you can’t tell the difference; (c) if you give them a kick they go the same direction; (d) if you weigh them they both weigh something different; (e) if you drop them into a black hole they never come out. Now what does it mean to say things are identical from a quantum perspective? 1
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Suppose the complex probability amplitude for the state of two particles A and B is a function of their two coordinates r and A B r thus ) , ( B A r r . If the particles are identical then there is no physical variable that can distinguish between two states that differ only by the exchange of the 2 particles. We require at the least that the probability [which is the absolute square of the probability amplitude] for finding the particles at r A and B r is the same as finding them at and and : B r A r 2 2 ) , ( ) , ( A B B A r r r r . To ensure this we need the wave function after the particles are switched to differ only by a phase whose absolute square is one: ) , ( } exp{ ) , ( B A A B r r i r r . What happens if we switch the particles again?
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This note was uploaded on 06/08/2009 for the course PHYS 2c taught by Professor All during the Spring '08 term at UC Riverside.

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PHYSICS 002C Lecture 25 - PHYSICS 002C Lecture 25 May 29,...

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