کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1855352 1529954 2007 26 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A quantum exactly solvable non-linear oscillator with quasi-harmonic behaviour
موضوعات مرتبط
مهندسی و علوم پایه فیزیک و نجوم فیزیک و نجوم (عمومی)
پیش نمایش صفحه اول مقاله
A quantum exactly solvable non-linear oscillator with quasi-harmonic behaviour
چکیده انگلیسی

The quantum version of a non-linear oscillator, previously analyzed at the classical level, is studied. This is a problem of quantization of a system with position-dependent mass of the form m = (1 + λx2)−1 and with a λ-dependent non-polynomial rational potential. This λ-dependent system can be considered as a deformation of the harmonic oscillator in the sense that for λ → 0 all the characteristics of the linear oscillator are recovered. First, the λ-dependent Schrödinger equation is exactly solved as a Sturm–Liouville problem, and the λ-dependent eigenenergies and eigenfunctions are obtained for both λ > 0 and λ < 0. The λ-dependent wave functions appear as related with a family of orthogonal polynomials that can be considered as λ-deformations of the standard Hermite polynomials. In the second part, the λ-dependent Schrödinger equation is solved by using the Schrödinger factorization method, the theory of intertwined Hamiltonians, and the property of shape invariance as an approach. Finally, the new family of orthogonal polynomials is studied. We prove the existence of a λ-dependent Rodrigues formula, a generating function and λ-dependent recursion relations between polynomials of different orders.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Annals of Physics - Volume 322, Issue 2, February 2007, Pages 434–459
نویسندگان
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