The trigonometric Rosen–Morse potential in the supersymmetric quantum mechanics and its exact solutions

Compean, C. B.; Kirchbach, Mariana

doi:10.1088/0305-4470/39/3/007

Cited by 75 publications

(104 citation statements)

References 10 publications

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“…The sequences and λ , = 1 2 can then be evaluated using (8). These quantities, for fixed and V 0 , are functions of the parameter E and the variable .…”

Section: The Standard Asymptotic Iteration Methodsmentioning

confidence: 99%

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Exact and approximate solutions of Schrödinger’s equation for a class of trigonometric potentials

2013

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Abstract:The asymptotic iteration method is used to find exact and approximate solutions of Schrödinger's equation for a number of one-dimensional trigonometric potentials (sine-squared, double-cosine, tangent-squared, and complex cotangent). Analytic and approximate solutions are obtained by first using a coordinate transformation to reduce the Schrödinger equation to a second-order differential equation with an appropriate form. The asymptotic iteration method is also employed indirectly to obtain the terms in perturbation expansions, both for the energies and for the corresponding eigenfunctions.PACS (

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“…The sequences and λ , = 1 2 can then be evaluated using (8). These quantities, for fixed and V 0 , are functions of the parameter E and the variable .…”

Section: The Standard Asymptotic Iteration Methodsmentioning

confidence: 99%

“…In this section we discuss a quasi-exact trigonometric potential model with complex coefficients [8],…”

Section: Complex Cotangent Potential Wellmentioning

confidence: 99%

Exact and approximate solutions of Schrödinger’s equation for a class of trigonometric potentials

2013

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“…We indeed follow here a recent approach to the wavefunctions of the latter potential for constant mass [42], which has stressed the interest of employing such polynomials, solutions of the second-order differential equation…”

Section: Resultsmentioning

confidence: 99%

Point Canonical Transformation versus Deformed Shape Invariance for Position-Dependent Mass Schrödinger Equations

Quesne¹

2009

SIGMA

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Abstract. On using the known equivalence between the presence of a position-dependent mass (PDM) in the Schrödinger equation and a deformation of the canonical commutation relations, a method based on deformed shape invariance has recently been devised for generating pairs of potential and PDM for which the Schrödinger equation is exactly solvable. This approach has provided the bound-state energy spectrum, as well as the ground-state and the first few excited-state wavefunctions. The general wavefunctions have however remained unknown in explicit form because for their determination one would need the solutions of a rather tricky differential-difference equation. Here we show that solving this equation may be avoided by combining the deformed shape invariance technique with the point canonical transformation method in a novel way. It consists in employing our previous knowledge of the PDM problem energy spectrum to construct a constant-mass Schrödinger equation with similar characteristics and in deducing the PDM wavefunctions from the known constantmass ones. Finally, the equivalence of the wavefunctions coming from both approaches is checked.

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“…There are many methods for solving Schrodinger equation, i.e. perturbation theory [1], the variational method [1], and the WKB method [1], Supersymmetry quantum mechanics [2]- [6], Nikivorov-Uvarov method [7]- [9], Romanovski polynomials in quantum mechanics [10]- [12], etc. [12]- [23].…”

Section: Introductionmentioning

confidence: 99%

Calculation of the Approximate Energy of Ground and Excited Stationary States in Quantum Mechanics Using Delta Method

Payandeh¹,

Mohammadpour²

2016

JAMP

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In this paper, pursuing a new advised method called Delta method which is basically similar to variational method, we find the ground and excited states, according to a typical quantum Hamiltonian. Moreover, applying this method, the upper bound values for the eigenenergies of the socalled ground and excited states are estimated. We will show that this new method, is as beneficial as the traditional variational method which is common in deriving eigenenergies of some of the quantum Hamiltonians. This method helps physics students to broaden their knowledge about the possible mathematical ways; they can use to obtain eigenenergies of some quantum Hamiltonians. The advantage of Delta method to variational method is in its simplicity and reduction of the calculation procedures.

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The trigonometric Rosen–Morse potential in the supersymmetric quantum mechanics and its exact solutions

Cited by 75 publications

References 10 publications

Exact and approximate solutions of Schrödinger’s equation for a class of trigonometric potentials

Exact and approximate solutions of Schrödinger’s equation for a class of trigonometric potentials

Point Canonical Transformation versus Deformed Shape Invariance for Position-Dependent Mass Schrödinger Equations

Calculation of the Approximate Energy of Ground and Excited Stationary States in Quantum Mechanics Using Delta Method

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