Quantum Physics in the Context of Countable and Uncountable Infinite Sets from the Perspective of Real Analysis

Gabriel Costa Vieira Arantes

Polytechnic and Arts School, Pontifical Catholic University of Goiás, Brazil.

Clóves Gonçalves Rodrigues *

Polytechnic and Arts School, Pontifical Catholic University of Goiás, Brazil.

*Author to whom correspondence should be addressed.


Abstract

This study aims to investigate countable and uncountable infinite sets from the perspective of real analysis. Key theorems and definitions related to this topic are presented, along with some specific applications in quantum physics, such as the quantization of energy, the relationships between the discrete and the continuous, and the hypothesis of the linearity of the Schrödinger wave equation.

Keywords: Quantum physics, infinite sets, countable sets, uncountable sets, real analysis


How to Cite

Arantes, G. C. V., & Rodrigues , C. G. (2023). Quantum Physics in the Context of Countable and Uncountable Infinite Sets from the Perspective of Real Analysis . Physical Science International Journal, 27(6), 65–74. https://doi.org/10.9734/psij/2023/v27i6814

Downloads

Download data is not yet available.

References

Lang S. Undergraduate Analysis. 2th ed. Springer; 2005.

Cantor G. Contributions to the founding of the theory of transfinite numbers. New York: Dover Publications; 1915. Available:https://archive.org/details/contributionstot003626mbp/page/n1/mode/2up

Apostol TM. Calculus: One-Variable calculus with an introduction to Linear Algebra. New York: Wiley. 1991;1(2).

Bartle RG, Sherbert DR. Introduction to Real Analysis. New York: Wiley; 2000.

Royden HL. Real Analysis, 3rd ed. New York: Macmillan Publishing Company; 1988.

Kossak R, Schmerl J. The structure of models of Peano Arithmetic. Oxford: Clarendon Press; 2006.

Terence T. Infinite sets, in: Analysis I. Texts and Readings in Mathematics. Singapore: Springer. 2016;37(3):181–210. Available:https://doi.org/10.1007/978-981-10-1789-6_8.

Brin M, Stuck G. Introduction to Dynamical Systems. Cambridge: Cambridge University Press; 2015.

Mehra J, Rechenberg H. The Historical Development of Quantum Theory. New York: Springer-Verlag.1982;1.

Kangro H. Early History of the Planck’s Radiation Law. London: Taylor & Francis; 1976.

Eisberg R, Resnick R. Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles. New York: Wiley; 1974;2.

Merzbacher E. Quantum Mechanics. Singapore: Wiley International; 1970.

Codata. The NIST Reference on Constants, Units, and Uncertainty. NIST. Available:https://physics.nist.gov/cgi-bin/cuu.

Tannoudji CC, Bernard D, Laloë F. Quantum Mechanics. and. New York: John Wiley & Sons; 1977;1(2).

Stepanov BI. Gustav Robert Kirchhoff (on the ninetieth anniversary of his death). J. Appl. Spectrosc. 1977;27:1099.

Gontijo LMA, Rodrigues CG. Thermal radiation and Planck’s formula. Quím. Nova. 2022;45(10):1303-1314. Available:https://doi.org/10.21577/0100-4042.20170942

Kangro H. Planck’s Original Papers in Quantum Physics, London: Taylor & Francis; 1972.

Millikan RA. A direct photoelectric determination of Planck’s “h”. Phys. Rev. 1916;7;355.

Rayleigh L. Remarks upon the law of complete radiation. Phil. Mag. 1900;49: 539.