Trigonometric Rosen–Morse Potential
The trigonometric Rosen–Morse potential, named after the physicists Nathan Rosen and Philip M. Morse, is among the exactly solvable quantum mechanical potentials. Definition In dimensionless units and modulo additive constants, it is defined as where r is a relative distance, \lambda is an angle rescaling parameter, and R is so far a matching length parameter. Another parametrization of same potential is which is the trigonometric version of a one-dimensional hyperbolic potential introduced in molecular physics by Nathan Rosen and Philip M. Morse and given by, a parallelism that explains the potential's name. The most prominent application concerns the V_^(\chi) parametrization, with \ell non-negative integer, and is due to Schrödinger who intended to formulate the hydrogen atom problem on Albert Einstein's closed universe, R^1\otimes S^3, the direct product of a time line with a three-dimensional closed space of positive constant curvature, the hypersphere S^, and ...
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