RATIONALLY EXTENDED SHAPE INVARIANT POTENTIALS IN ARBITRARY D DIMENSIONS ASSOCIATED WITH EXCEPTIONAL Xm POLYNOMIALS
نویسندگان
چکیده
منابع مشابه
Infinitely many shape invariant potentials and new orthogonal polynomials
Three sets of exactly solvable one-dimensional quantum mechanical potentials are presented. These are shape invariant potentials obtained by deforming the radial oscillator and the trigonometric/hyperbolic Pöschl-Teller potentials in terms of their degree l polynomial eigenfunctions. We present the entire eigenfunctions for these Hamiltonians (l = 1, 2, . . .) in terms of new orthogonal polynom...
متن کاملA Coherent State Associated with Shape-invariant Potentials * †
An algebraic treatment of shape-invariant potentials is discussed. By introducing an operator which reparametrizes wave functions, the shape-invariance condition can be related to a generalized Heisenberg-Weyl algebra. It is shown that this makes it possible to define a coherent state associated with the shape-invariant potentials.
متن کاملCyclic 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...
متن کاملShape invariant potentials with PT symmetry
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...
متن کاملShape - invariant potentials and an associated coherent state
An algebraic treatment of shape-invariant potentials in supersymmetric quantum mechanics is discussed. By introducing an operator which reparametrizes wave functions, the shape-invariance condition can be related to a oscillator-like algebra. It makes possible to define a coherent state associated with the shape-invariant potentials. For a large class of such potentials, it is shown that the in...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Acta Polytechnica
سال: 2017
ISSN: 1805-2363,1210-2709
DOI: 10.14311/ap.2017.57.0477