Optical reflection from planetary surfaces as an operator-eigenvalue problem

Physics

Scientific paper

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Eigenvalues, Limb Darkening, Lunar Surface, Optical Reflection, Planetary Surfaces, Reciprocity Theorem, Boundary Conditions, Boundary Value Problems, Hermitian Polynomial, Maxwell Equation, Quantum Mechanics

Scientific paper

The utility of a theory framed in terms of operators and their eigenvalue equations, as related to the reciprocity principle in diffuse reflection, is investigated. A superposition of the eigenfunctions found from a solution by separation of variables was inadequate to form a general solution that can be fitted to a one-dimensional boundary condition because of the difficulty of resolving the reciprocity operator into a superposition of independent one-dimensional operators. This problem is illustrated by a failed prediction of limb-darkening of the full moon from brightness versus phase. A general solution is derived which fully exploits the determinative powers of the reciprocity operator as an unresolved two-dimensional operator. A close association is found between the reciprocity operator and the particle-exchange operator of quantum mechanics.

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