Bound states of the Klein–Gordon equation with vector and scalar Rosen–Morse-type potentials

Liu, Yi; Yong-feng, Diao; Liu, Jianyi; Jia, Chun‐Sheng

doi:10.1016/j.physleta.2004.10.054

Cited by 155 publications

(108 citation statements)

References 39 publications

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“…After the following mapping on the potential parameter: 1 1 V V in (56), the results in (69) and (70) become identical with (13) and (14) of [52]. …”

Section: The Rosen-morse-type Modelmentioning

confidence: 74%

“…which is identical with those given in Equation (22) of [52] under the equally-mixed potential restriction given by    .…”

mentioning

confidence: 65%

“…The s-wave bound-state solution of the Schrödinger equation for the Eckart potential has been widely investigated by using various methods, such as the supersymmetric (SUSY) shape invariance technology [49], point canonical transformation (PCT) method [50] and SUSY Wentzel-Kramers-Brillouin (WKB) approximation approach [51]. The bound state solutions of the s-wave Klein-Gordon (KG) equation with equally mixed Rosen-Morse-type (Eckart and Rosen--Morse well) potentials have been studied [52]. The bound state solutions of the s-wave Dirac equation with equal vector and scalar Eckart-type potentials in terms of the basic concepts of the shape-invariance approach in the SUSYQM have also been studied [34][35][36][37].…”

Section: Introductionmentioning

confidence: 99%

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Bound States of the Klein-Gordon for Exponential-Type Potentials in D-Dimensions

Ikhdair¹

2011

JQIS

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The approximate analytic bound state solutions of the Klein-Gordon equation with equal scalar and vector exponential-type potentials including the centrifugal potential term are obtained for any arbitrary orbital quantum number l and dimensional space D. The relativistic/non-relativistic energy spectrum formula and the corresponding un-normalized radial wave functions, expressed in terms of the Jacobi polynomials

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“…After the following mapping on the potential parameter: 1 1 V V in (56), the results in (69) and (70) become identical with (13) and (14) of [52]. …”

Section: The Rosen-morse-type Modelmentioning

confidence: 74%

“…which is identical with those given in Equation (22) of [52] under the equally-mixed potential restriction given by    .…”

mentioning

confidence: 65%

Section: Introductionmentioning

confidence: 99%

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Bound States of the Klein-Gordon for Exponential-Type Potentials in D-Dimensions

Ikhdair¹

2011

JQIS

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“…Recently, many works about the Dirac or the Klein-Gordon (KG) equation with scalar and vector potentials of equal magnitude (SVPEM) are reported [1,2,3,4,5,6,7,8,9,10,11,12] .When the potentials are spherical, the Dirac equation is said to have the spin or pseudospin symmetry corresponding to the same or opposite sign. These symmetries, which have been observed in the hadron and nuclear spectroscopies for a long time [13,14], are derived from the investigation of the dynamics between a quark and an antiquark [15,16].…”

Section: Introductionmentioning

confidence: 99%

Dynamical symmetries of the Klein–Gordon equation

Zhang

Chen

2009

Journal of Mathematical Physics

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The dynamical symmetries of the two-dimensional Klein-Gordon equations with equal scalar and vector potentials (ESVP) are studied. The dynamical symmetries are considered in the plane and the sphere respectively. The generators of the SO(3) group corresponding to the Coulomb potential, and the SU (2) group corresponding to the harmonic oscillator potential are derived.Moreover, the generators in the sphere construct the Higgs algebra. With the help of the Casimir operators, the energy levels of the Klein-Gordon systems are yielded naturally.

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“…For various types of potentials, such as linear, exponential, Coulomb, Rosen-Morse, etc., the exact bound state solutions of the one-dimensional Klein-Gordon equation have been reported. [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] It is also reported that the onedimensional Klein-Gordon equation can be exactly solved for shape invariant potentials.…”

Section: Introductionmentioning

confidence: 99%

Quantization Rule for Relativistic Klein-Gordon Equation

Sun¹

2011

Bulletin of the Korean Chemical Society

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Based on the exact quantization rule for the nonrelativistic Schrödinger equation, the exact quantization rule for the relativistic one-dimensional Klein-Gordon equation is suggested. Using the new quantization rule, the exact relativistic energies for exactly solvable potentials, e.g. harmonic oscillator, Morse, and Rosen-Morse II type potentials, are obtained. Consequently the new quantization rule is found to be exact for one-dimensional spinless relativistic quantum systems. Though the physical meanings of the new quantization rule have not been fully understood yet, the present formal derivation scheme may shed light on understanding relativistic quantum systems more deeply.

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Bound states of the Klein–Gordon equation with vector and scalar Rosen–Morse-type potentials

Cited by 155 publications

References 39 publications

Bound States of the Klein-Gordon for Exponential-Type Potentials in D-Dimensions

Bound States of the Klein-Gordon for Exponential-Type Potentials in D-Dimensions

Dynamical symmetries of the Klein–Gordon equation

Quantization Rule for Relativistic Klein-Gordon Equation

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