Path integral solution for a deformed radial Rosen–Morse potential

Kadja, A; Benamira, F.; Guéchi, L.

doi:10.1007/s12648-016-0916-8

Cited by 5 publications

(5 citation statements)

References 31 publications

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“…as a good approximation for 1 r 2 in the centrifugal potential term when |q| ≥ 1 as it can be seen in Fig. 2 which contains a plot of 1 (αr) 2 and of 1 3…”

Section: Green's Functionmentioning

confidence: 64%

“…The potentials V q (r) and S q (r) are equal and of the form (see, for example Ref. [1] and references therein)…”

Section: Introductionmentioning

confidence: 99%

“…where V 1 , V 2 , α and q are four ajustable real parameters, V 1 and V 2 describe the depth of the potential well, α is the screening parameter related to the range of the potential characterized by the length α −1 . The expression (1) is defined in terms of q−deformed hyperbolic functions sinh q x = e x − qe −x 2 , cosh q x = e x + qe −x 2 , tanh q x = sinh q x cosh q x (2)…”

Section: Introductionmentioning

confidence: 99%

“…Also, for −1 ≤ q < 0 or q > 0, various methods have been used to solve the Klein-Gordon and Dirac equations [14,15,16,17,18] with these same potentials. In particular, for |q| = 1 and for a light modification of expression (1), the relativistic rotational-vibrational energies and the radial wave functions have been approximately calculated with the help of the supersymmetric WKB approach and through the resolution of the Klein-Gordon equation [19]. More recently, the usefulness of the Manning-Rosen potential and the Rosen-Morse potential for calculations of the vibrational partition function to study the thermodynamic properties of diatomic molecules has been emphasized by Jia and co-workers [20,21].…”

Section: Introductionmentioning

confidence: 99%

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Path integral solution for a Klein–Gordon particle in vector and scalar deformed radial Rosen–Morse-type potentials

et al. 2017

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The problem of a Klein-Gordon particle moving in equal vector and scalar Rosen-Morse-type potentials is solved in the framework of Feynman's path integral approach. Explicit path integration leads to a closed form for the radial Green's function associated with different shapes of the potentials. For q ≤ −1, and 1 2α ln |q| < r < +∞, the energy equation and the corresponding wave functions are deduced for the l states using an appropriate approximation to the centrifugal potential term. When −1 < q < 0 or q > 0, it is shown that the quantization conditions for the bound state energy levels En r are transcendental equations which can be solved numerically. Three special cases such as the standard radial Manning-Rosen potential (|q| = 1), the standard radial Rosen-Morse potential (V2 → −V2, q = 1) and the radial Eckart potential (V1 → −V1, q = 1) are also briefly discussed.

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“…as a good approximation for 1 r 2 in the centrifugal potential term when |q| ≥ 1 as it can be seen in Fig. 2 which contains a plot of 1 (αr) 2 and of 1 3…”

Section: Green's Functionmentioning

confidence: 64%

“…The potentials V q (r) and S q (r) are equal and of the form (see, for example Ref. [1] and references therein)…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Path integral solution for a Klein–Gordon particle in vector and scalar deformed radial Rosen–Morse-type potentials

et al. 2017

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“…The propagator P RM (u ′′ , u ′ ; Λ) is none other than that relating to the Rosen-Morse potential [36,37] (general modified Poschl-Teller potential) defined in terms of deformed hyperbolic functions as well…”

Section: Construction Of the Path Integralmentioning

confidence: 99%

Non-relativistic bound state solutions of a linear combination of deformed Hulthén plus generalized Kratzer potentials using Feynman path integral approach

Sadoun

Haddad

2023

Preprint

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The approximate bound state solutions of Schrödinger equation with linear combination of a q-deformed Hulthén potential plus screened Kratzer potential were obtained with the help of appropriate approximation to evaluate the centrifugal term. The Feynman path integral approach was used to obtain the analytical solutions. The energy spectrum and the normalized wave functions of the bound states are derived from the poles of the Green’s function and its residues. Particular cases of these potentials are also discussed briefly and it is found that obtained results are in good agreement with those obtained in the literature.

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Supersymmetric approach to approximate analytical solutions of the Klein-Gordon equation: application to a position-dependent mass and a hyperbolic cotangent vector potential

Zaghou,

Benamira

2023

Indian J Phys

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Path integral solution for a deformed radial Rosen–Morse potential

Cited by 5 publications

References 31 publications

Path integral solution for a Klein–Gordon particle in vector and scalar deformed radial Rosen–Morse-type potentials

Path integral solution for a Klein–Gordon particle in vector and scalar deformed radial Rosen–Morse-type potentials

Non-relativistic bound state solutions of a linear combination of deformed Hulthén plus generalized Kratzer potentials using Feynman path integral approach

Supersymmetric approach to approximate analytical solutions of the Klein-Gordon equation: application to a position-dependent mass and a hyperbolic cotangent vector potential

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