Planck function defined

Planck function - A thermodynamic function defined by T = -GIT, where G is Gibbs energy and T thermodynamic temperature. [2]... 

This expression is valid for the transition from the state i with energy Ej to the state / with energy Ef, where hcbif = Ef — Ei, Na is the Avogadro constant, h is Planck s constant, c is the speed of light in vacuum, k is the Boltzmann constant, Cq is the permittivity of free space, and, finally, Q is the partition function defined as g = 6xp(—Uy/kr), where gj is the total... 

In this equation, H, the Hamiltonian operator, is defined by H = — (h2/8mir2)V2 + V, where h is Planck s constant (6.6 10 34 Joules), m is the particle s mass, V2 is the sum of the partial second derivative with x,y, and z, and V is the potential energy of the system. As such, the Hamiltonian operator is the sum of the kinetic energy operator and the potential energy operator. (Recall that an operator is a mathematical expression which manipulates the function that follows it in a certain way. For example, the operator d/dx placed before a function differentiates that function with respect to x.) E represents the total energy of the system and is a number, not an operator. It contains all the information within the limits of the Heisenberg uncertainty principle, which states that the exact position and velocity of a microscopic particle cannot be determined simultaneously. Therefore, the information provided by Tint) is in terms of probability I/2 () is the probability of finding the particle between x and x + dx, at time t. 

Before embarking on this discussion one fact must be established. In many applications the autocorrelation function of L(t) is not really a delta function, but merely sharply peaked with a small rc > 0. Accordingly L(t) is a proper stochastic function, not a singular one. Then (4.5) is a well-defined stochastic differential equation (in the sense of chapter XVI) with a well-defined solution. If one now takes the limit rc —> 0 in this solution, it becomes a solution of the Stratonovich form (4.8) of the Fokker-Planck equation. This theorem has been proved officially, but the result can also be seen as follows. 

Since a molecule has translational, rotational, vibrational and electronic energy levels it is possible to define q for all four cases. Vibrational energy e is given hy e = hv, where h is Planck s constant, and V the frequency of vibration. The vibrational partition function q is then obtained by taking the sum over all tihe vibrational energy levels defined by the vibrational quantum number v. This is... 

Radiation emitted by the lamp is caused by the temperature achieved by its filament, which in turn depends on the power input on the lamp. The radiation spectral distribution is a function of the temperature of the source and the wavelength, and this relationship is defined by the Planck black body equation ... 

Planck-Einstein function which occurs in c (T), it is possible to define a temperature T such that for most practical purposes... 

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