magazinelogo

Journal of Applied Mathematics and Computation

ISSN Print: 2576-0645 Downloads: 153802 Total View: 1839639
Frequency: quarterly ISSN Online: 2576-0653 CODEN: JAMCEZ
Email: jamc@hillpublisher.com
Article Open Access http://dx.doi.org/10.26855/jamc.2022.12.002

Angular Momentum and Orbital Degrees of Freedom of s Electrons in an Atom—A New Quantum Theoretical Insight

K. Iyakutti1,*, V. J. Surya1, Y. Kawazoe1,2,3

1Department of Physics and Nanotechnology, SRM Institute of Science and Technology, SRM Nagar, Kattankulathur, 603203, Kanchipuram, Chennai, TN, India.

2New Industry Creation Hatchery Center, Tohoku University, Aramaki, Sendai 980-8579, Japan.

3Department of Physics, Suranaree University of Technology, Nakhon, Ratchasima, Thailand.

*Corresponding author: K. Iyakutti

Published: November 3,2022

Abstract

Assigning dimension to θ on par with r, in the wave function Ψ(r,θ), we have quantum engineered the orbital angular momentum and the corresponding orbital degrees of freedom of s electrons. The quantized orbital angular momentum of s electron in an atom is estimated as 0.75ћ2 using angular momentum engineering.  This restoration of orbital angular momentum leads to new additional quantum numbers to s electrons and there is a possibility for the alteration of s electron occupation. This newly discovered s electron property can be invoked where ever the present quantum theory is inadequate to explain some of the exotic properties observed in modern materials.

References

[1] Y. Cao, V. Fatemi , S. Fang, K. Watanabe , T. Taniguchi , E. Kaxiras , P. Jarillo-Herrero. Nature 556, 43 (2018).

[2] K. Gotlieb, C.Y. Lin, M. Serbyn, W. Zhang, C.L. Smallwood, C. Jozwiak, H. Eisaki, Zahid Hussain, A. Vishwanath, A. Lanzara. Science, 362 (6420), 1271 (2018). 

[3] A. P. Drozdov, P. P. Kong, V. S. Minkov, S. P. Besedin, M. A. Kuzovnikov, S. Mozaffari,L. Balicas, F. F. Balakirev, D. E. Graf, V. B. Prakapenka, E. Greenberg, D. A. Knyazev, M. Tkacz & M. I. Eremets. Nature, 569, 528 (2019).

[4] E. Snider, N. Dasenbrock-Gammon, R. McBride, M. Debessai, H. Vindana, K. Vencatasamy, K. V. Lawler, A. Salamat, and R. P. Dias. Nature, 586, 373 (2020).

[5] C. J. Pickard, I. Errea and M. I. Eremets, Annu. Rev. Condens. Matter Phys. 11, 57 (2020). 

[6] M. Ekholm, D. Gambino, H.J.M. Jönsson, F. Tasnádi, B. Alling, I.A. Abrikosov, Phys. Rev. B98, art. 094413 (2018). 

[7] Fu Y. and Singh D. J. (2018). “Applicability of the Strongly Constrained and Appropriately Normed Density Functional to Tran-sition-Metal Magnetism”, Phys. Rev. Lett. 121, art. 207201. 

[8] T.A.Hamlin, I. Fernandez and Bickelhaupt, Angew Chem., Int. Ed. 58, 8922 (2019).

[9] J.H. Belo, A.L. Pires, I.T. Gomes, V. Andrade, J.B. Sousa, R.L. Hadimani, D.C. Jiles, Y. Ren, X. Zhang, J.P. Araújo, and A.M. Pereira Phys. Rev. B 100, 134303 (2019).

[10] Z. Zheng, Q. Ma, Z. Bi, S. Barrera, M.H. Liu, N. Mao, Y. Zhang, N. Kiper, K. Watanabe, T. Taniguchi, J. Kong, W.A. Tisdale, R. Ashoori, N. Gedik, L. Fu, S.Y. Xu and P. Jarillo-Herrero. Nature volume 588, 71 (2020).

[11] J.E. Romain, Angle as the fourth fundamental quantity. J. Res. Nat. Bur. Stds. 66B, 97 (1962). 

[12] K.R. Brownstein. Am. J. Phys. 65(7), 605 (1997). 

[13] D. Bolton. Comments in Mathematics 106 (2016). https://www.physicsforums.com/insights/can-angles-assigned- dimension/.

[14] K. Iyakutti, Y. Kawazoe, V.J. Surya, I. Lakshmi and R. Rajeswarapalanichamy. Int. Journal of Comput. Mat. Science and Eng. 09(1), Art. 2050003 (2020). 

[15] L.I. Schiff. Quantum Mechanics, p.7, (McGraw-Hill Book Company, INC, New York, 1949). 

[16] V. Devanathan. “Angular Momentum Techniques in Quantum Mechanics”, Springer Science & Business Media, Kindle Edition, 2006.

[17] Glendinning I. (2010). “Rotations on the Bloch Sphere”, https://www.bloch-sphere-rotations.pdf.

[18] M. Briggeman, M. Tomczyk, B.Tian, H. Lee, J. Lee, Y.He, A.Tylan-Tyler, M. Huang, C.Eom, D. Pekker, R.S.K. Mong, P. Irvin, J. Levy. Science 367, 769 (2020). 

[19] Y. Zhang, C. Lane, J.W. Furness , B. Barbiellinic, J.P. Perdew, R.S. Markiewicz, A. Bansil, and J. Sun. PNAS. 117 (1), 68 (2020). 

[20] Z. Zheng, Q. Ma, Z. Bi, S. Barrera, M.H. Liu, N. Mao, Y. Zhang, N. Kiper, K. Watanabe, T. Taniguchi, J. Kong, W.A. Tisdale, R. Ashoori, N. Gedik, L. Fu, S.Y. Xu, P. Jarillo-Herrero. Nature, 588 (7836) 71 (2020).

[21] T.J.Volz, S.J. Turneaure, S.M. Sharma and Y.M. Gupta. Phys. Rev. B 101, art. 224109 (2020).

[22] K. Iyakutti, M. Rajarajeswari and Y. Kawazoe. Physica B 405, 3324 (2010).

[23] K. Kaiser, L.M. Scriven, F. Schulz, P. Gawel, L. Gross, H.L. Anderson Science, 365 (6459), 1299 (2020). 

[24] S. Xu, F. Liu, J. Xu, Y. Cui and C. Wang. Journal of Molecular Modeling 26, Art.111 (2020).

[25] K. Iyakutti, V.J. Surya, I. Lakshmi, R. Rajeswarapalanichamy, Y. Kawazoe. Materials Science and Engineering: B 263, 114895 (2021).

How to cite this paper

Angular Momentum and Orbital Degrees of Freedom of s Electrons in an Atom—A New Quantum Theoretical Insight

How to cite this paper:  K. Iyakutti, V. J. Surya, Y. Kawazoe. (2022) Angular Momentum and Orbital Degrees of Freedom of s Electrons in an Atom—A New Quantum Theoretical Insight. Journal of Applied Mathematics and Computation6(4), 405-409.

DOI: http://dx.doi.org/10.26855/jamc.2022.12.002