Page 85 - IJOCTA-15-1
P. 85
Conformable Schr¨odinger equation in D-dimensional space
case D ≤ 3 and β ≤ 1. For D is an integer and [8] Sylvere, A. S., David, V., Justin, M., Joseph, M.,
β = 1, we arrive at the same results as in the Betchewe, G., & Inc, M. (2023). Modulational in-
traditional solutions. stability in lossless left-handed metamaterials in
nonlinear Schr¨odinger equation with non-integer
Acknowledgments dimensional space. Modern Physics Letters B,
37(11), 2350002. https://doi.org/10.1142/
None. S0217984923500021
[9] Awoga, O. A., & Ikot, A. N. (2012). Approximate
Funding solution of Schr¨odinger equation in D dimensions
for inverted generalized hyperbolic potential. Pra-
None. mana, 79, 345–356. https://doi.org/10.1007/
s12043-012-0328-z
Conflict of interest [10] Pe˜na, J. J., Garc´ıa-Mart´ınez, J., Garc´ıa-Ravelo,
J., & Morales, J. (2015). Bound state solu-
The authors declare that they have no conflict of
tions of D-dimensional schr¨odinger equation with
interest regarding the publication of this article.
exponential-type potentials. International Jour-
nal of Quantum Chemistry, 115(3), 158-164. ht
Author contributions
tps://doi.org/10.1002/qua.24803
[11] El-Nabulsi, R. A. (2021). Quantum dynamics in
Conceptualization: All authors
low-dimensional systems with position-dependent
Formal analysis: All authors
mass and product-like fractal geometry. Phys-
Methodology: All authors
ica E: Low-Dimensional Systems and Nanostruc-
Writing – original draft: All authors
tures, 134, 114827. https://doi.org/10.1016/
Writing – review & editing: All authors j.physe.2021.114827
[12] Fisher, M. E. (1974). The renormalization group
Availability of data in the theory of critical behavior. Reviews of Mod-
ern Physics, 46(4), 597. https://doi.org/10.1
Not applicable.
103/RevModPhys.46.597
[13] Mandelbrot, B. B. (1989). Fractal geometry:
References
what is it, and what does it do?. Proceedings
[1] Mandelbrot, B.B, (1983). The Fractal Geometry of the Royal Society of London. A. Mathematical
of Nature/Ed. WH Freeman. New York. and Physical Sciences, 424(1864), 3–16. https:
[2] He, X-F. (1990). Anisotropy and isotropy: A //doi.org/10.1098/rspa.1989.0038
model of fraction-dimensional space. Solid State [14] Sun, J. (2023). Fractal modification of
Communications, 75(2), 111-114. https://doi. Schr¨odinger equation and its fractal variational
org/10.1016/0038-1098(90)90352-C principle. Thermal Science, 27(3 Part A). 2029–
[3] He, X-F. (1990). Fractional dimensionality and 2037. https://doi.org/10.2298/TSCI2303029S
fractional derivative spectra of interband optical [15] El-Nabulsi, R. A., & Anukool, W. (2021). Quan-
transitions. Physical Review B, 42(18), 11751. ht tum dots and cuboid quantum wells in fractal
tps://doi.org/10.1103/PhysRevB.42.11751 dimensions with position-dependent masses. Ap-
[4] Muslih, S. I. & Baleanu, D. (2007). Fractional plied Physics A, 127, 1–15. https://doi.org/10
multipoles in fractional space. Nonlinear Analy- .1007/s00339-021-04989-6
sis: Real World Applications, 8(1), 198-203. http [16] Matos-Abiague, A., Oliveira, L. E., & de Dios-
s://doi.org/10.1016/j.nonrwa.2005.07.001 Leyva, M. (1998). Fractional-dimensional ap-
[5] Sadallah, M., & Muslih, S. I. (2009).Solution of proach for excitons in G a A s- G a 1- x Al x As
the equations of motion for Einstein’s field in frac- quantum wells. Physical Review B, 58(7), 4072.
tional D dimensional space-time. International [17] Reyes-G´omez, E., Matos-Abiague, A., Perdomo-
Journal of Theoretical Physics, 48, 3312–3318. ht Leiva, C. A., de Dios-Leyva, M., & Oliveira, L. E.
tps://doi.org/10.1007/s10773-009-0133-8 (2000). Excitons and shallow impurities in G a A
[6] Ahmad, S., Zubair, M., & Younis, U. (2022). Cap- s- G a 1- x Al x As semiconductor heterostruc-
turing of non-hydrogenic Rydberg series of ex- tures within a fractional-dimensional space ap-
citon binding energy in two-dimensional mono- proach: Magnetic-field effects. Physical Review B,
layer WS2 using a modified Coulomb potential in 61(19), 13104.
fractional space. Physica Scripta, 98(1), 015106. [18] Jarlskog, C., & Yndur´ain, F.J. (1986). Is the num-
https://doi.org/10.1088/1402-4896/acaa6a ber of spatial dimensions an integer?. Europhysics
[7] Khan, S., Khan, F. M. A., Gulalai, & Noor, A. Letters, 1(2), 51. https://doi.org/10.1209/02
(2023). General solution for electromagnetic wave 95-5075/1/2/002
propagation in cylindrical waveguide filled with [19] Schafer, A., & Muller, B. (1986). Bounds for the
fractional space . Waves in Random and Com- fractal dimension of space. Journal of Physics A:
plex Media, 33(1), 49–61. https://doi.org/10 Mathematical and General, 19(18), 3891. https:
.1080/17455030.2021.1874076 //doi.org/10.1088/0305-4470/19/18/034
79

