A quantum particle in a circle; an informational approach revisited
DOI:
https://doi.org/10.31349/RevMexFis.71.040701Keywords:
Particle in a circle; Shannon entropy; Fisher information; disequilibriumAbstract
We study the localization-delocalization of a particle moving within a circular region of radius r0 from a theoretical information point of view. We computed the Shannon entropy, Fisher information and disequilibrium in configuration and momentum spaces for a collection of stationary states. Comparing our results of Shannon entropies with those previously published we found good agreement with those. Shannon entropy, Fisher information and the disequilibrium offer complementary results for the description of the particle localization-delocalization.
References
Y. Wang, Seismic Inversion: Theory and Applications. (Wiley Blackwell: Hoboken, NJ, USA, 2016)
A. Srivastava, Stochastic models for capturing image variability. IEEE Signal Process. Mag., 19 (2002) 63, https://doi.org/10.1109/MSP.2002.1028353
F. Grosshans and N. J. Cerf, Continuous-variable quantum cryptography is secure against non-gaussian attacks. Phys. Rev. Lett., 92 (2004) 047905, https://doi.org/10.1103/PhysRevLett.92.047905
A. D. Wyner and S. Shamai, Introduction to communication in the presence of noise by c. e. shannon. Proc. IEEE, 86 (1998) 442, https://doi.org/10.1109/jproc.1998.659496
J. Huang, T. Supaongprapa, I. Terakura, F. Wang, N. Ohnishi, and N. Sugie, A model-based sound localization system and its application to robot navigation. Rob. Aut. Syst., 27 (1999) 199, https://doi.org/10.1016/S0921-8890(99)00002-0
M. Prato and L. Zanni, Inverse problems in machine learning: An application to brain activity interpretation. J. Phys.: Conf. Ser., 135 (2008) 012085, https://doi.org/10.1088/1742-6596/135/1/012085
F. del Río, R. López-Hernández, and C. Chaparro-Velázquez, On information, entropy, and early stone tools. Mol. Phys., e2310644 (2024) 00268976, https://doi.org/10.1080/00268976.2024.2310644
R. Casadio, R. da Rocha, P. Meert, L. Tabarroni, and W. Barreto, Configurational entropy of black holes quantum cores. Class. Quantum Grav., 40 (2023) 075014, https://doi.org/10.1088/1361-6382/acbe89
Z. Chen, C. S.Wannere Corminboeuf, R. Puchta, and P. R. V. Schleyer, Nucleus-independent chemical shifts (ncis) as an aromaticity criterion. Chem. Rev., 105 (2005) 3842, https://doi.org/10.1021/cr030088+.
G. Maroulis, M. Sana, and G. Leroy, Molecular properties and basis set quality: An approach based on information theory. Int. J. Quantum Chem., 19 (1981) 43, https://doi.org/10.1002/qua.560190106
A. M. Simas, A. J. Takkar, and V. H. Smith, Basis set quality, ii. information theoretic apparaisal of various s-orbitals. Int. J. Quantum Chem., 24 (1983) 527, https://doi.org/10.1002/qua.560240603
S. R. Gadre, S. B. Sears, S. J. Chakravorty, and R. B. Bendale, Some novel characteristics of atomic information entropies. Phys. Rev. A, 32 (1985) 2602, https://doi.org/10.1103/PhysRevA.32.2602
M. Ho, R. P. Sagar, H. Schmider, D. F. Weaver, and B. H. Smith Jr., Measures of distance for atomic charge and momentum densities and their relationship to physical properties. Int. J. Quantum Chem., 53 (1994) 627, https://doi.org/10.1002/qua.560530606
P. Fuentealba and J. Melin, Atomic spin density polarization index and atomic spin-density information entropy distance. Int. J. Quantum Chem., 90 (2002) 334, https://doi.org/10.1002/qua.994
R. Atre, A. Kumar, and R. P. Panigraph, Quantum information entropies of the eigenstates and the coherent state of the poschl- ¨ teller potential. Phys. Rev. A, 69 (2004) 052107, https://doi.org/10.1103/PhysRevA.69.052107
. 16. J. S. Dehesa, A. Martinez-Finkelstein, and V. N. Sorokin. Information theoretic measures for morse and pöschl-teller potentials. Mol. Phys., 104 (2006) 613, https://doi.org/10.1080/00268970500493243
M. W. Coffey, Semiclassical position and momentum information entropy for sech2 and a family of rotational potentials. Can. J. Phys., 85 (2013) 733, https://doi.org/10.1139/p07-062
G. H. Sun and S. H. Dong, Quantum information entropies of the eigenstates for a symmetrically trigonometric rosenmorse potential. Phys. Scr., 87 (2013) 045003, https://doi.org/10.1088/0031-8949/87/04/045003
G. H. Sun, S. H. Dong, and S. Naad, Quantum information entropies for an asymmetric trigonometric rosen-morse potential. Ann. Phys. (Berlin), 525 (2013) 934, https://doi.org/10.1002/andp.201300089
E. Aydiner, C. Orta, and R. Sever, Quantum information entropies of the eigenstates of the morse potential, Int. J. Mod. Phys. B, 22 (2008) 231, https://doi.org/10.1142/S021797920803848X
I. Nasser and A. Abdel-Hady, Fisher information and Shannon entropy calculations for two-electron systems. Can. J. Phys., 98 (2020) 784, https://doi.org/10.1139/cjp-2019-0391
I. Nasser, C. Mart´ınez-Flores, M. Zeama, R. Vargas, and J. Garza. Tsallis entropy: A comparative study for the 1s2-state of helium atom. Phys. Lett. A, 392 (2021) 127136, https://doi.org/10.1016/j.physleta.2020.127136
R. Joshi, N. Verma, and M. Mohan, Shannon entropy along hydrogen isoelectronic sequence using numerov method. Rev. Mex. F´ıs., 69 (2023) 060401, https://doi.org/10.31349/RevMexFis.69.060401
R. González-Férez and J. S. Dehesa, Characterization of atomic avoided crossings by means of Fisher’s information. The European Physical Journal D, 32 (2005) 39, https://doi.org/10.1140/epjd/e2004-00182-3
R. W. Robinet, Visualizing the solutions for the circular infinite well in quantum and classical mechanics, Am. J. Phys., 64 (1996) 440, https://doi.org/10.1119/1.18188
R. W. Robinet, Visualizing the solutions for the circular infinite well in quantum and classical mechanics. Am. J. Phys., 64 (1996) 440
R. Y. Agcali, B. Atik, E. Bilgen, B. Karli, and M. F. Danisman, Leading to a better understanding of the particle-in-aquantum-corral model. J. Chem. Educ., 96 (2019) 82, https://doi.org/10.1021/acs.jchemed.8b00622
X. D. Song, G. H. Sun, and S. H. Dong, Shannon information entropy for an infinite circular well. Physics Letters A, 379 (2015) 1402, https://doi.org/10.1016/j.physleta.2015.03.020
H. H. Corzo, E. Castaño, H. G. Laguna, and R. P. Sagar, Measuring localization-delocalization phenomena in a quantum corral. J. Math Chem, 51 (2012) 179, https://doi.org/10.1007/s10910-012-0073-z
E. Cruz, N. Aquino, and V. Prasad, Localization-delocalization of a particle in a quantum corral in presence of a constant magnetic field. Eur. Phys. J. D, 75 (2021) 106, https://doi.org/10.1140/epjd/s10053-021-00119-2
T. B. Tai, R. W. A. Havenith, J. L. Teunissen, A. R. Dok, S. D. Hallaert, M. T. Nguyen, and A. Ceulemans, Particle on a boron disk: Ring currents and disk aromaticity in B20 2−, Inorganic Chemistry, 52 (2013) 10595, https://doi.org/10.1021/ic401596s
I. Bialynicki-Birula and Rudnicki, Entropic uncertainty relations in quantum physics in K. D. Sen (editor), Statistical Complexity; applica- tions in electronic structure. (Springer, London, 2011), Chap. 1
N. Aquino and E. Casta no, La partícula dentro de una caja circular. Contactos, 26 (1998) 11
J. Rey Pastor and A. de Castro Brzezicki, Funciones de Bessel, teoría matemática y aplicaciones a la ciencia y a la técnica. (Ed. DOSSAT S. A., España 1958)
M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, Chap. 9. (Dover Publications INC, New York, 1972)
NIST digital library of Mathematical Functions, Chap. 10. https://dlmf.nist.gov/
W. S. Nascimento and F. V. Prudente, Shannon entropy: A study of confined hydrogenic-like atoms. Chem. Phys. Lett., 691 (2018) 401, https://doi.org/10.1016/j.cplett.2017.11.048
Neetik Mukherjee, Sangita Majumdar, and Amlan K. Roy. Fisher information in confined hydrogen-like ions. Chem. Phys. Lett., 691 (2018) 449, https://doi.org/10.1016/j.cplett.2017.11.059
K. D. Sen, Characteristic features of shannon information entropy of confined atoms. J. Chem. Phys., 123 (2005) 074110, https://doi.org/10.1063/1.2008212
N. Aquino, A. Flores-Riveros, and J. F. Rivas-Silva, Shannon and fisher entropies for a hydrogen atom under soft spherical confinement. Phys. Lett. A., 377 (2013) 2062, https://doi.org/10.1016/j.physleta.2013.05.048
M. Rodríguez Bautista, R. Vargas, N. Aquino, and J.Garza, Electrondensity delocalization in many-electron atoms confined by penetrable walls: A hartree-fock study. Int. J. Quantum Chem., 118 (2017) e25571, https://doi.org/10.1002/qua.25571
C. R. Estañón, N. Aquino, D. Puertas-Centeno, and J. S. Dehesa, Twodimensional confined hydrogen: An entropy and complexity approach. Int. J. Quantum Chem., 120 (2020) e26192, https://doi.org/10.1002/qua.26192
W. S. Nascimento and F. V. Prudente, Sobre um estudo da entropía de shannon no contexto da mecanica quántica: uma aplicacao ao oscilador harmonico livre e confinado. Quim Nova, 39 (2016) 757, https://doi.org/10.5935/0100-4042.20160045
C. R. Estañón, H. E. Montgomery Jr., J. C. Angulo, and N. Aquino, The confined helium atom: An information-theoretic approach. Int. J. Quantum Chem., 124 (2024) e27358, https://doi.org/10.1002/qua.27358
S. Majumdar and A. K. Roy, Shannon entropy in confined helium-like ions within a density functional formalism. Quantum Rep., 2 (2020) 189, https://doi.org/10.3390/quantum2010012
I. Nasser, M. Zeama, and A. Abdel-Hady, Renyi, fisher, shannon and their electron correlation tools for two-electron series. Phys. Scr. 95 (2020) 095401, https://doi.org/10.1088/1402-4896/abaa09
C. Martínez-Flores, Shannon entropy and fisher information for endohedral one an two-electron atoms. Phys. Lett. A, 386 (2021) 126988, https://doi.org/10.1016/j.physleta.2020.126988
F. C. E. Lima, A. R. P. Moreira, C. A. S. Almeida, C. O. Edet, and N. Ali. Quantum information entropy of a particle trapped by the aharonov-bohmtype effect, Phys. Scr., 98 (2023) 065111, https://doi.org/10.1088/1402-4896/acd309
I. Bialynicki-Birula and J. Mycielski, Uncertainty relations for information entropy in wave mechanics. Commun. Math. Phys., 44 (1975) 129, https://doi.org/10.1007/ BF01608825
P. Sánchez-Moreno, A. R. Plastino, and J. S. Dehesa, A quantum uncertainty relation based on Fisher’s information. J. Phys. A: Math. Theor., 44 (2011) 065301, https://doi.org/10.1088/1751-8113/44/6/065301
S. López-Rosa, J. C. Angulo, and J. Antolin, Rigorous properties and uncertainty-like relationships on product-complexity measures: Aplication to atomic systems. Physica A, 388 (2009) 2081, https://doi.org/10.1016/j.physa.2009.01.037
O. Onicescu. C. R. Acad, Theorie de l’information energie informationelle, Sci. Paris A, 263 (1966) 25
J. C. Angulo, J. Antolın, and K. D. Sen, Fisher-shannon plane and statistical complexity of atoms. Physics Letters A, 372 (2008) 670, https://doi.org/10.1016/j.physleta.2007.07.077
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 E. Cruz, N. Aquino, C. R. Estañón, H. Yee-Madeira

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Authors retain copyright and grant the Revista Mexicana de Física right of first publication with the work simultaneously licensed under a CC BY-NC-ND 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.