Virial Theorem and Scaling Analysis in Infinitely Confined Quantum Dots

Celalettin Demir

doi:10.17776/csj.1855648

Virial Theorem and Scaling Analysis in Infinitely Confined Quantum Dots

Abstract

The virial theorem is a fundamental principle giving the relationship between kinetic and potential energies in classical and quantum mechanical systems. In this study, the virial theorem was investigated using the scaling method in quantum dot structures. Two different approaches were used; the wave function of the position vector was scaled only in the first approach, while the dot radius was scaled only in the second approach. This method is valid not only for single-electron systems but can also be applied to multi-electron systems. In the calculations, the virial theorem was satisfied. Furthermore, the average energy of the system was minimized, and so on demonstrating that this approach provides a highly accurate and stable framework for multi-electron systems.

Keywords

Energy optimization, Quantum dots, Scaling, Virial theorem

References

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Details

Primary Language

English

Subjects

Atomic and Molecular Physics

Journal Section

Research Article

Authors

Celalettin Demir ^*
0000-0002-0393-5931
Türkiye

Publication Date

April 29, 2026

Submission Date

January 4, 2026

Acceptance Date

March 12, 2026

Published in Issue

Year 2026 Volume: 47 Number: 2

DOI

https://doi.org/10.17776/csj.1855648

IZ

https://izlik.org/JA47AM88FW

APA

Demir, C. (2026). Virial Theorem and Scaling Analysis in Infinitely Confined Quantum Dots. Cumhuriyet Science Journal, 47(2), 366-372. https://doi.org/10.17776/csj.1855648

AMA

1.Demir C. Virial Theorem and Scaling Analysis in Infinitely Confined Quantum Dots. CSJ. 2026;47(2):366-372. doi:10.17776/csj.1855648

Chicago

Demir, Celalettin. 2026. “Virial Theorem and Scaling Analysis in Infinitely Confined Quantum Dots”. Cumhuriyet Science Journal 47 (2): 366-72. https://doi.org/10.17776/csj.1855648.

EndNote

Demir C (April 1, 2026) Virial Theorem and Scaling Analysis in Infinitely Confined Quantum Dots. Cumhuriyet Science Journal 47 2 366–372.

IEEE

[1]C. Demir, “Virial Theorem and Scaling Analysis in Infinitely Confined Quantum Dots”, CSJ, vol. 47, no. 2, pp. 366–372, Apr. 2026, doi: 10.17776/csj.1855648.

ISNAD

Demir, Celalettin. “Virial Theorem and Scaling Analysis in Infinitely Confined Quantum Dots”. Cumhuriyet Science Journal 47/2 (April 1, 2026): 366-372. https://doi.org/10.17776/csj.1855648.

JAMA

1.Demir C. Virial Theorem and Scaling Analysis in Infinitely Confined Quantum Dots. CSJ. 2026;47:366–372.

MLA

Demir, Celalettin. “Virial Theorem and Scaling Analysis in Infinitely Confined Quantum Dots”. Cumhuriyet Science Journal, vol. 47, no. 2, Apr. 2026, pp. 366-72, doi:10.17776/csj.1855648.

Vancouver

1.Celalettin Demir. Virial Theorem and Scaling Analysis in Infinitely Confined Quantum Dots. CSJ. 2026 Apr. 1;47(2):366-72. doi:10.17776/csj.1855648

As of 2026, Cumhuriyet Science Journal will be published in six issues per year, released in February, April, June, August, October, and December

Virial Theorem and Scaling Analysis in Infinitely Confined Quantum Dots

Abstract

Keywords

References

Details

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Acceptance Date

Published in Issue

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