Question

A system of 6 identical 1-dimensional harmonic oscillators (it could be two atoms of an Einstein...

A system of 6 identical 1-dimensional harmonic oscillators (it could be two atoms of an Einstein model solid). What is the probability that the first oscillator has 2 quanta of vibrational energy when the system has 3 quanta of vibrational energy?

Hint: You may find it useful to consider how many microstates the system has and how many microstates the rest of the system has when the first oscillator has 2 quanta.

Answer is 5/56

For the system considered in the previous problem the probability that the first oscillator has 0 quanta of vibrational energy is?

Answer is: greater than the probability that it has 2 quanta

How do I get these answers?

Thanks for your help!

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Homework Answers

Answer #1

No. of microstates in which first oscillator has 2 quanta of energy and other oscillators has 1 quanta of energy is 5, because one quanta can be given to any 5 other oscillators.

Now total microstates are

1)1 oscillator has 2 quanta and any of the others have 1 quanta = 30microstates

2) 1 oscillator has 3 quanta, rest has 0 quanta=6 microstates.

3)3 oscillators having 1 quanta each =20 microstates.

Total=56

So probability is 5/56

The probability that the 1st oscillator has 0 quanta is greater than the previous answer as there are contributions from each of the 3 distribution types.There are lot many micro states where 1st oscillator has 0 quanta.

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