Generalized Ladder Operators for Shape-invariant Potentials
نویسندگان
چکیده
منابع مشابه
Generalized Ladder Operators for Shape-invariant Potentials
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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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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متن کاملar X iv : h ep - t h / 04 05 01 3 v 1 3 M ay 2 00 4 Ladder operators for subtle hidden shape invariant potentials
Ladder operators can be constructed for all potentials that present the integrability condition known as shape invariance, satisfied by most of the exactly solvable potentials. Using the superalgebra of supersymmetric quantum mechanics we construct the ladder operators for two exactly solvable potentials that present a subtle hidden shape invariance. PACS No. 03.65.Fd, 11.30.Pb, 31.15.Pf
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ژورنال
عنوان ژورنال: Physica Scripta
سال: 2001
ISSN: 0031-8949,1402-4896
DOI: 10.1238/physica.regular.064a00548