Field-free Hamiltonian energy distribution

CO. If f/is viewed as divisible without limit, then an infinite number of distributions are possible. Planck considered U as made up of an entirely determined number of finite equal parts of value fia. This quantization of the electromagnetic radiation leads to the concept of photons of energy quanta fico, each of which having a Hamiltonian of the form of a harmonic oscillator. A state of the free electromagnetic field is specified by the number, n, for each of such oscillators and n then corresponds to the number of photons in a state with energy fico. Photons obey Bose-Einstein statistics. Denote by the number of photons with energy... 

Combinatorial quantities such as entropy and free energy, which depend on the entire distribution of states sampled, require further effort to extract. Methods based on thermodynamic relations which express these quantities as integrals over ensemble averages of mechanical quantities, e.g., dH(X)ldX, where 1 defines the state at which the Hamiltonian is evaluated, are most often used to extract thermal properties [14]. X may be temperature, volume, or even a change in the force field itself. 

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