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Chapter: 1 / Q: 3
Obtain an expression for the third moment of a binomial distribution. What is the behavior of this moment for large N?
Chapter: 1 / Q: 4
Consider an event of probability p. The probability of n occurrences of this event out of N trials is given by the binomial distribution
Chapter: 5 / Q: 6
A set of N classical oscillators in one dimension is given by the Hamiltonian
Chapter: 5 / Q: 7
Consider again the preceding problem. The canonical par- tition function can be written as an integral form,
Chapter: 5 / Q: 8
A system of N one-dimensional localized oscillators, at a given temperature T , is associated with the Hamiltonian
Chapter: 6 / Q: 1
A system of N classical ultrarelativistic particles, in a con- tainer of volume V , at temperature T , is given by the Hamil- tonian
Chapter: 6 / Q: 2
Consider a set of N one-dimensional harmonic oscillators, described by the Hamiltonian
Chapter: 6 / Q: 3
Consider a classical system of N very weakly interacting diatomic molecules, in a container of volume V , at a given tem- perature T . The Hamiltonian of a single molecule is given by
Chapter: 6 / Q: 4
Neglecting the vibrational motion, a diatomic molecule may be treated as a three-dimensional rigid rotator. The Hamil- tonian
Chapter: 6 / Q: 5
Consider a classical gas of N weakly interacting molecules, at temperature T ,
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