Shape-invariant potentials depending onnparameters transformed by translation
نویسندگان
چکیده
منابع مشابه
Cyclic Shape Invariant Potentials
We formulate and study the set of coupled nonlinear differential equations which define a series of shape invariant potentials which repeats after a cycle of p iterations. These cyclic shape invariant potentials enlarge the limited reservoir of known analytically solvable quantum mechanical eigenvalue problems. At large values of x, cyclic superpotentials are found to have a linear harmonic osc...
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Exact reflection and transmission coefficients for supersymmetric shapeinvariant potentials barriers are calculated by an analytical continuation of the asymptotic wave functions obtained via the introduction of new generalized ladder operators. The general form of the wave function is obtained by the use of the F(−∞,+∞)-matrix formalism of Fröman and Fröman which is related to the evolution of...
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Shape invariance is an important ingredient of many exactly solvable quantum mechanics. Several examples of shape invariant “discrete quantum mechanical systems” are introduced and discussed in some detail. They arise in the problem of describing the equilibrium positions of Ruijsenaars-Schneider type systems, which are “discrete” counterparts of Calogero and Sutherland systems, the celebrated ...
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A general form for ladder operators is used to construct a method to solve bound-state Schrödinger equations. The characteristics of supersymmetry and shape invariance of the system are the start point of the approach. To show the elegance and the utility of the method we use it to obtain energy spectra and eigenfunctions for the one-dimensional harmonic oscillator and Morse potentials and for ...
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Suitable complexification of the well known hyperbolic Rosen Morse oscillator in one dimension is shown to give the fourth (and last?) exactly solvable model which combines the shape and PT invariance. PACS 03.65.Ge, 03.65.Fd Review paper [1] emphasizes that a requirement of the so called shape invariance (with respect to the translation of a parameter) determines all the four known exactly sol...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and General
سال: 2000
ISSN: 0305-4470,1361-6447
DOI: 10.1088/0305-4470/33/17/305