Exact solution of Schrödinger equation in (anti-)de Sitter spaces for hydrogen atom

Falek, Mokhtar; Belghar, Nourredine; Moumni, Mustafa

doi:10.1140/epjp/s13360-020-00337-4

Cited by 9 publications

(6 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To obtain the value of k, the term under the square root sign in ( 10) is set to zero [43]. Subsequently, by solving (7) and ( 11), we obtained the energy eigenvalue equation.…”

Section: Review Of Nikiforov-uvarov (Nu) Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Analytical Investigation of the Single-Particle Energy Spectrum in Magic Nuclei of ⁵⁶Ni and ¹¹⁶Sn

et al. 2020

View full text Add to dashboard Cite

The analytical solutions of the radial D-dimensional Schrödinger equation for the Yukawa potential plus spin-orbit and Coulomb interaction terms are presented within the framework of the Nikiforov-Uvarov method by using the Greene-Aldrich approximation scheme to the centrifugal barrier. The energy eigenvalues obtained are employed to calculate the single-energy spectrum of ⁵⁶Ni and ¹¹⁶Sn for distinct quantum states. We have also obtained corresponding normalized wave functions for the magic nuclei manifested in terms of Jacobi polynomials. However, the energy spectrum without Spin-orbit and Coulomb interaction terms precisely matches the quantum mechanical system of the Yukawa potential field at any arbitrary state.

show abstract

“…To obtain the value of k, the term under the square root sign in ( 10) is set to zero [43]. Subsequently, by solving (7) and ( 11), we obtained the energy eigenvalue equation.…”

Section: Review Of Nikiforov-uvarov (Nu) Methodsmentioning

confidence: 99%

“…The Schrodinger equation in Ddimensionional space of nucleons which interacts with each other is of the form [43]:…”

Section: Solution Of the Schrodinger Equation With Yukawa Potential Plus Spin-orbit And Coulomb Interaction Termsmentioning

confidence: 99%

Analytical Investigation of the Single-Particle Energy Spectrum in Magic Nuclei of ⁵⁶Ni and ¹¹⁶Sn

et al. 2020

View full text Add to dashboard Cite

show abstract

“…Some problems have also been solved in non-relativistic quantum mechanics; this was done despite the fact that we can not derive any nonrelativistic covariant Schrödinger-like equation from the covariant Klein-Fock-Gordon equation in the traditional field theory method of deSitter (dS) and anti-deSitter (AdS) models. Here, we use the EUP formulation to write the Schrödinger equation version for both dS and AdS cases [12][13][14].…”

Section: Introductionmentioning

confidence: 99%

2D Relativistic Oscillators with a Uniform Magnetic Field in Anti-deSitter Space

Sek,

Falek,

Moumni

2021

Preprint

Self Cite

View full text Add to dashboard Cite

We study analytically the two-dimensional deformed bosonic oscillator equation for charged particles (both spin 0 and spin 1 particles) subject to the effect of an uniform magnetic field. We consider the presence of a minimal uncertainty in momentum caused by the Anti-de Sitter model and we use the Nikiforov-Uvarov (NU) method to solve the system. The exact energy eigenvalues and the corresponding wave functions are analytically obtained for both Klein Gordon and scalar Duffin-Kemmer-Petiau (DKP) cases. For spin 1 DKP case, we deduce the behavior of the DKP equation and write the non-relativistic energies and we show the fundamental role of the spin in this case. Finally, we study the thermodynamic properties of the system.

show abstract

“…In this context, we can use the EUP formulation to write the dS and AdS versions of the Schrödinger equation. Indeed, we find the treatment of the exact solution of the D-dimensional Schrödinger equation for the free particle and the harmonic oscillator in AdS space [12], the study, with perturbative methods, of the implications of extended uncertainty principle of dS Space on the spectrums of both harmonic oscillator and hydrogen atom [13] and the exact solution of the Schrödinger equation for the hydrogen atom in dS and AdS spaces [14].…”

Section: Introductionmentioning

confidence: 99%

Exact Solutions of the DKP Oscillator in 3D Spaces with Extended Uncertainty Principle

Falek¹,

Moumni²,

Merad³

2020

Preprint

Self Cite

View full text Add to dashboard Cite

We present the exact solution of the three-dimensional Duffin-Kemmer-Petiau oscillator for both spin 0 and spin 1 cases, with the presence of minimal uncertainty in momentum in anti-de Sitter model. We use the representation of vector spherical harmonics and the Nikiforov-Uvarov method to determine exactly the energy eigenvalues and the eigenfunctions in all cases. Our study of the energy spectrum allows us to define a new interpretation of natural and unnatural parity states of the vector particle and we show the crucial role played by the spin-orbit coupling in this differentiation between the parities.

show abstract

Exact solution of Schrödinger equation in (anti-)de Sitter spaces for hydrogen atom

Cited by 9 publications

References 35 publications

Analytical Investigation of the Single-Particle Energy Spectrum in Magic Nuclei of ⁵⁶Ni and ¹¹⁶Sn

Analytical Investigation of the Single-Particle Energy Spectrum in Magic Nuclei of ⁵⁶Ni and ¹¹⁶Sn

2D Relativistic Oscillators with a Uniform Magnetic Field in Anti-deSitter Space

Exact Solutions of the DKP Oscillator in 3D Spaces with Extended Uncertainty Principle

Contact Info

Product

Resources

About