445lec16 - PHYS 445 Lecture 16 Quantum oscillators Lecture...

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PHYS 445 Lecture 16 - Quantum oscillators 16 - 1 © 2001 by David Boal, Simon Fraser University. All rights reserved; further resale or copying is strictly prohibited. Lecture 16 - Quantum oscillators What's Important: quantum oscillator at T > 0 continuous quantum states Text : Reif Quantum oscillators In the previous lecture we used the classical equipartition theorem to establish that the mean energy of a single oscillator in one dimension is equal to k B T . But we know that the energy states of a quantum oscillator are discrete, not continuous. How does this effect its behavior at finite temperature? The energy levels of a quantum oscillator are equally spaced, by an amount h / 2 π , where obeys the classical frequency formula = ( k/m ) 1/2 . That is For quantum number n , the corresponding energy is E n = ( n + 1/2) h / 2 π . One route to obtain the mean energy for this system is to use the partition function, which now involves a sum over (nicely spaced) discrete states:
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This note was uploaded on 09/07/2009 for the course PHYS 445 taught by Professor Davidboal during the Spring '08 term at Simon Fraser.

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445lec16 - PHYS 445 Lecture 16 Quantum oscillators Lecture...

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