Exact solution of the Klein–Gordon equation in the presence of a minimal length

Jana, Tapas Kumar; Roy, Provas Kumar

doi:10.1016/j.physleta.2009.02.007

Cited by 44 publications

(33 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In contrast, conditionally exact solutions are generated only for specific values of the potential parameters and for quasi-exact solutions, only part of the energy spectrum is determined. Exact solutions of the Dirac equation in the presence of different potentials were obtained in the past [2][3][4][5] using various theoretical techniques.…”

Section: Introductionmentioning

confidence: 99%

Solving Dirac equation using the tridiagonal matrix representation approach

2016

View full text Add to dashboard Cite

Abstract:The aim of this work is to find exact solutions of the one-dimensional Dirac equation that do not belong to the already known conventional class. We write the spinor wavefunction as a bounded infinite sum in a complete basis set, which is chosen such that the matrix representation of the Dirac wave operator becomes tridiagonal and symmetric. This makes the wave equation equivalent to a symmetric three-term recursion relation for the expansion coefficients of the wavefunction. We solve the recursion relation and obtain the relativistic energy spectrum and corresponding state functions. Restriction to the diagonal representation results in the conventional class of solutions. As illustration, we consider the square well with half-sine potential bottom in the vector and scalar coupling under spin symmetry. We obtain the relativistic energy spectrum and show that the nonrelativistic limit agrees with results found elsewhere.

show abstract

Section: Introductionmentioning

confidence: 99%

Solving Dirac equation using the tridiagonal matrix representation approach

2016

View full text Add to dashboard Cite

show abstract

“…In relativistic equations, the minimal length was introduced in the Dirac equation, with a constant magnetic field [22,23], with vector and scalar linear potentials [24], for the hydrogen atom potential [25], and the Dirac oscillator [26,27]. The effect of the GUP was also investigated in the context of the Klein-Gordon equation [22,28,29]. Finally, the Casimir effect [30,31], and the black body radiation [32] have been studied within this modified formalism of quantum mechanics.…”

Section: Introductionmentioning

confidence: 99%

Pseudoharmonic oscillator in quantum mechanics with a minimal length

Bouaziz

Boukhellout

2014

Mod. Phys. Lett. A

View full text Add to dashboard Cite

The pseudoharmonic oscillator potential is studied in non relativistic quantum mechanics with a generalized uncertainty principle characterized by the existence of a minimal length scale, (∆x) min = √ 5β. By using a perturbative approach, we derive an analytical expression of the energy spectrum in the first order of the minimal length parameter β. We investigate the effect of this fundamental length on the vibration-rotation energy levels of diatomic molecules through this potential function interaction. We explicitly show that the minimal length would have some physical importance in studying the spectra of diatomic molecules. * Electronic address: djamilbouaziz@univ-jijel.dz † Electronic address: abdelmalek-boukhellout@univ-jijel.dz

show abstract

“…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%

“…(22). But using the method for finding the superpotential of shape invariant potentials suggested by Cooper and Ginocchio, 31 one may obtain the superpotential W(x) and consequently the ground state effective energy E 1,0 .…”

mentioning

confidence: 99%

Quantization Rule for Relativistic Klein-Gordon Equation

Sun¹

2011

Bulletin of the Korean Chemical Society

View full text Add to dashboard Cite

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.

show abstract

Exact solution of the Klein–Gordon equation in the presence of a minimal length

Abstract: We obtain exact solutions of the (1 + 1) dimensional Klein Gordon equation with linear vector and scalar potentials in the presence of a minimal length. Algebraic approach to the problem has also been studied.

Cited by 44 publications

References 32 publications

Solving Dirac equation using the tridiagonal matrix representation approach

Solving Dirac equation using the tridiagonal matrix representation approach

Pseudoharmonic oscillator in quantum mechanics with a minimal length

Quantization Rule for Relativistic Klein-Gordon Equation

Contact Info

Product

Resources

About