Arbitrary l-state solutions of the rotating Morse potential through the exact quantization rule method

Qin, Wen; Dong, Shi‐Hai

doi:10.1016/j.physleta.2006.10.091

Cited by 173 publications

(146 citation statements)

References 14 publications

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“…However, analytical solutions are possible only in a few simple cases such as the hydrogen atom and the harmonic oscillator [1,2]. Most quantum systems could be solved only by using approximation schemes like rotating Morse potential via Pekeris approximation [3][4][5] and the generalized Morse potential by means of an improved approximation scheme [6]. Recently, the study of exponential-type potentials has attracted much attention from many authors (for example, cf, ).…”

Section: Introductionmentioning

confidence: 99%

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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Section: Introductionmentioning

confidence: 99%

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

Ikhdair¹

2011

JQIS

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“…Woods-Saxon potential for more than a decade has been of practical interest especially as it is widely used in nuclear nuclear physics to describe nuclear shell model [17][18][19][20]. Nuclear shell model describes the interaction of nucleon with heavy nucleus [21][22][23].…”

Section: Q-deformed Woods-saxon Plus Modified Coulomb Potentialmentioning

confidence: 99%

Exact Bound State Solution of Qdeformed Woods-Saxon Plus Modified Coulomb Potential Using Conventional NIKIFOROV-UVAROV Method

Okon¹,

Popoola²,

Isonguyo³

2014

IJRAP

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In this work, we obtained an exact solution to Schrodinger equation using q-deformed Woods-Saxon plus modified Coulomb potential Using conventional Nikiforov-Uvarov method. We also obtained the energy eigen value and its associated total wave function . This potential with some suitable conditions reduces to two well known potentials namely: the Yukawa and coulomb potential. Finally, we obtained the numerical results for energy eigen value with different values of q as dimensionless parameter. The result shows that the values of the energies for different quantum number(n) is negative(bound state condition) and increases with an increase in the value of the dimensionless parameter(arbitrary constant). The graph in figure (1) shows the different energy levels for a particular quantum number. KEYWORDSSchrodinger, Nikiforov-Uvarov method, Woods-Saxon potential plus modified exponential potential.

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“…The effective potential or potential-like term V eff (x) is apparently energy dependent so that the iterative method should be used to solve Eq. (7). But, in all the previous works, the E n in V eff (x) is assumed to be constant, i.e.…”

Section: -27mentioning

confidence: 99%

“…Nonetheless for exactly solvable potentials, the exact energies obtained from the quantization rule have been reported. [5][6][7][8][9][10] The quantization rule cannot be algebraically derived from the Schrödinger equation but the Schrödinger equation is utilized in the process of deducing the rule.…”

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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Arbitrary l-state solutions of the rotating Morse potential through the exact quantization rule method

Cited by 173 publications

References 14 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

Exact Bound State Solution of Qdeformed Woods-Saxon Plus Modified Coulomb Potential Using Conventional NIKIFOROV-UVAROV Method

Quantization Rule for Relativistic Klein-Gordon Equation

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