Shannon entropy as an indicator for the orbital shape manipulation of a hydrogen atom under a repulsive single barrier potential
DOI:
https://doi.org/10.31349/SuplRevMexFis.6.011305Keywords:
Hydrogen atom, Potential barrier, Shannon information entropy, Lagrange mesh methodAbstract
The effect of a penetrable repulsive single-barrier potential on the structural properties of hydrogen atom in ground and different excited (n,l) states [n=1-3, l=0-2] is studied. The Lagrange mesh method is adopted to solve the corresponding Schrodinger equation numerically for energy eigenvalues and eigenfunctions. Different novel features and phenomena e.g. shrinking the size of the atom, atomic swelling, orbital fusion and fission etc. are noted when the strength of the barrier is changed by tuning its position and height. It is remarkable that all such alterations of the atomic orbital are well articulated from the Shannon entropy profile.
References
A.Michels, J. De Boer, and A.Bijl, Remarks concerning molecular interaction and their influence on the polarisability, Physica 4 (1937) 981, https://doi.org/10.1016/S0031-8914(37)80196-2
A. Sommerfeld and H. Welker, Künstliche Grenzbedingungen beim Keplerproblem, Ann. Phys. 424 (1938) 56, https://doi.org/10.1002/andp.19384240109
J. Sabin and E. Brändas, eds., Advances in Quantum Chemistry, vol. 58 (Academic Press, 2009), https://doi.org/10.1016/S0065-3276(09)00701-1
J. Sabin and E. Brändas, Advances in Quantum Chemistry: Theory of Confined Quantum Systems - Part Two, 58 of Advances in Quantum Chemistry, 1-297 (Academic Press, 2009). https://doi.org/10.1103/PhysRevA.110.042819
S. Mondal, A. Sadhukhan, K. Sen, and J. K. Saha, Stability of a two-electron system under pressure confinement: structural and quantum information theoretical analysis, J. Phys. B: At., Mol. Opt. Phys. 56 (2023) 155001, https://doi.org/10.1088/1361-6455/ace177
K. D. Chakladar, S. Mondal, K. Sen, and J. K. Saha, Quantuminformation-theoretic analysis of Zee systems under pressure confinement, Phys. Rev. A 110 (2024) 042819, https://doi.org/10.1103/PhysRevA.110.042819
S. Mondal, A. Sadhukhan, J. K. Saha, and A. K. Roy, Information-theoretic measures and Compton profile of H atom under finite oscillator potential, J. Phys. B: At., Mol. Opt. Phys. 57 (2024) 175001, https://dx.doi.org/10.1088/1361-6455/ad5fd3
V. Dolmatov and J. King, Atomic swelling upon compression, J. Phys. B: At., Mol. Opt. Phys. 45 (2012) 225003, https://dx.doi.org/10.1088/0953-4075/45/22/225003
V. K. Dolmatov, Confinement-induced orbital breathing, fusion, fission and re-ordering in semifilled shell atoms, J. Phys. B: At., Mol. Opt. Phys. 46 (2013) 095005, https://dx.doi.org/10.1088/0953-4075/46/9/095005
A. Nahum, J. Ruhman, and D. A. Huse, Dynamics of entanglement and transport in one-dimensional systems with quenched randomness, Phys. Rev. B 98 (2018) 035118, https://doi.org/10.1103/PhysRevB.98.035118
H. Barghathi, C. M. Herdman, and A. Del Maestro, Rényi Generalization of the Accessible Entanglement Entropy, Phys. Rev. Lett. 121 (2018) 150501, https://doi.org/10.1103/PhysRevLett.121.150501
P. Lévay, S. Nagy, and J. Pipek, Elementary formula for entanglement entropies of fermionic systems, Phys. Rev. A 72 (2005) 022302, https://doi.org/10.1103/PhysRevA.72.022302
A. Grassi, A relationship between atomic correlation energy of neutral atoms and generalized entropy, Int. J. Quantum Chem. 111 (2011) 2390, https://doi.org/10.1002/qua.22541
L. Delle Site, On the scaling properties of the correlation term of the electron kinetic functional and its relation to the Shannon measure, Europhys. Lett. 88 (2009) 19901, https://doi.org/10.1209/0295-5075/88/19901
L. M. Ghiringhelli, L. Delle Site, R. A. Mosna and I. P. Hamilton, Information-theoretic approach to kinetic-energy functionals: the nearly uniform electron gas, J. Math. Chem. 48 (2010) 78, https://doi.org/10.1007/s10910-010-9690-6
N. Flores-Gallegos, Informational energy as a measure of electron correlation, Chem. Phys. Lett. 666 (2016) 62, https://doi.org/10.1016/j.cplett.2016.10.075
M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, 2010), https://doi.org/10.1017/CBO9780511976667
D. S. Naik, C. G. Peterson, A. G. White, A. J. Berglund and P. G. Kwiat, Entangled State Quantum Cryptography: Eavesdropping on the Ekert Protocol, Phys. Rev. Lett. 84 (2000) 4733, https://doi.org/10.1103/PhysRevLett.84.4733
M.-J. Zhao, S.-M. Fei, and X. Li-Jost, Complete entanglement witness for quantum teleportation, Phys. Rev. A 85 (2012) 054301, https://doi.org/10.1103/PhysRevA.85.054301
M. G. A. Paris, Quantum Estimation for Quantum Technology, Int. J. Quantum Chem. 07 (2009) 125, https://doi.org/10.1142/S0219749909004839
C. E. Shannon, A mathematical theory of communication, Bell Sys. Tech. J. 27 (1948) 379, https://doi.org/10.1002/j.1538-7305.1948.tb01338.x
R. González-Férez and J. S. Dehesa, Characterization of atomic avoided crossings by means of Fisher’s information, Eur. Phys. J. D 32 (2005) 39, https://doi.org/10.1140/epjd/e2004-00182-3
A. Rényi, On Measures of Entropy and Information, Berkeley Symposium on Mathematical Statistics and Probability 4.1 (1961) 547 https://projecteuclid.org/ebook/Download?urlid=bsmsp/1200512181&isFullBook=false
C. Tsallis, Possible generalization of Boltzmann-Gibbs statistics, J. Stat. Phys. 52 (1988) 479, https://doi.org/10.1007/BF01016429
C. R. O. Onicescu, Possible generalization of Boltzmann-Gibbs statistics, Hebd. Seances Acad. Sci. A 263 (1966) 841, https://doi.org/10.1007/BF01016429
F. J. A. van Ruitenbeek, J. Goseling, H. W. Bakker, and A. A. K. Hein, Shannon Entropy as an Indicator for Sorting Processes in Hydrothermal Systems, Entropy 22 (2020) 656, https://doi.org/10.3390/e22060656
K.-W. Park, J. Kim, and S. Moon, Shannon Entropy as an Indicator of the Spatial Resolutions of the Morphologies of the Mode Patterns in an Optical Resonator, Curr. Opt. Photon. 5 (2021) 16 https://opg.optica.org/copp/abstract.cfm?URI=copp-5-1-16
S. Saha and J. Jose, Shannon entropy as an indicator of correlation and relativistic effects in confined atoms, Phys. Rev. A 102 (2020) 052824, https://doi.org/10.1103/PhysRevA.102.052824
R. González-Férez and J. S. Dehesa, Shannon Entropy as an Indicator of Atomic Avoided Crossings in Strong Parallel Magnetic and Electric Fields, Phys. Rev. Lett. 91 (2003) 113001, https://doi.org/10.1103/PhysRevLett.91.113001
Y. L. He, Y. Chen, J. N. Han, Z. B. Zhu, G. X. Xiang, H. D. Liu, B. H. Ma, and D. C. He, Shannon entropy as an indicator of atomic avoided crossings for Rydberg potassium atoms interacting with a static electric field, Eur. Phys. J. D. 69 (2015) 283, https://doi.org/10.1140/epjd/e2015-60397-7
C. Barrales-Martínez, R. Durán, and J. Caballero, Shannon entropy variation as a global indicator of electron density contraction at interatomic regions in chemical reactions, J. Mol. Model. 30 (2024) 371, https://doi.org/10.1007/s00894-024-06171-0
P. M. Cincotta et al., The Shannon entropy: An efficient indicator of dynamical stability, Phys. D: Nonlinear Phenomena 417 (2021) 132816, https://doi.org/10.1016/j.physd.2020.132816
H. W. Wijesekera and T. M. Dillon, Shannon entropy as an indicator of age for turbulent overturns in the oceanic thermocline, J. Geophys. Res. Oceans 102 (1997) 3279, https://doi.org/10.1029/96JC03605
J. P. Connerade, V. K. Dolmatov, and P. A. Lakshmi, The filling of shells in compressed atoms, J. Phys. B: At., Mol. Opt. Phys. 33 (2000) 251, https://dx.doi.org/10.1088/0953-4075/33/2/310
J. -P. Connerade, Confining and compressing the atom, Eur. Phys. J. D 74 (2020) 1, https://doi.org/10.1140/epjd/e2020-10414-y
D. Baye, Lagrange-mesh method for quantum-mechanical problems, Phys. Stat. Sol. (b) 243 (2006) 1095, https://doi.org/10.1002/pssb.200541305
P. Descouvemont, C. Daniel, and D. Baye, Three-body systems with Lagrange-mesh techniques in hyperspherical coordinates, Phys. Rev. C 67 (2003) 044309, https://doi.org/10.1103/PhysRevC.67.044309
M. Vincke, L. Malegat, and D. Baye, Regularization of singularities in Lagrange-mesh calculations, J. Phys. B: At., Mol. Opt. Phys. 26 (1993) 811, https://dx.doi.org/10.1088/0953-4075/26/5/006
L. G. Jiao, L. R. Zan, Y. Z. Zhang and Y. K. Ho, Benchmark values of Shannon entropy for spherically confined hydrogen atom, Int. J. Quan. Chem. 117 (2017) e25375, https://doi.org/10.1002/qua.25375
S. Mondal, A. Sadhukhan, K. Sen, and J. K. Saha, Structural properties and quantum information measures of H, Li and Na atoms endohedrally captured in C36 and C60 cages, Eur Phys J. P. 138 (2023) 576, https://doi.org/10.1140/epjp/s13360-023-04188-7
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