A basic derivation can be found here: http://books.Google.com/books?id=rpbdozIZt3sC&pg=PA128&lpg=PA128&dq=kramers+heisenberg+dispersion+formula&sour
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The Kramers-Heisenberg dispersion formula relates the refractive index to the absorption coefficient of a medium in terms of its wavelength. It is derived using quantum mechanical perturbation theory and is based on the assumption of a harmonic oscillator model for the electrons in the medium. The formula helps to explain how the refractive index and absorption properties of a material depend on the wavelength of light passing through it.
The equation that is not used in the derivation of the keyword is the quadratic formula.
The formula for calculating the angular momentum expectation value in quantum mechanics is L L, where L represents the angular momentum operator and is the wave function of the system.
The one-dimensional elastic collision formula is derived from the principles of conservation of momentum and conservation of kinetic energy. By applying these principles to the collision of two objects in one dimension, the formula can be derived to calculate the final velocities of the objects after the collision.
The reduced mass formula is used in physics to calculate the effective mass of two interacting objects. It is represented as (m1 m2) / (m1 m2), where m1 and m2 are the masses of the two objects. This formula is used in various physics calculations, such as in the study of celestial mechanics and quantum mechanics, to simplify the analysis of systems with multiple interacting objects.
The speed of sound in a medium is derived from the properties of the medium, such as its density and elasticity. It is calculated using the formula: speed of sound square root of (elasticity / density).