The Vector Hypercomplex Numbers and the Matter Waves

International Journal of Applied Physics

© 2022 by SSRG - IJAP Journal

Volume 9 Issue 2

Year of Publication : 2022

Authors : Vlad L. Negulescu

10.14445/23500301/IJAP-V9I2P103

How to Cite?

Vlad L. Negulescu, "The Vector Hypercomplex Numbers and the Matter Waves," SSRG International Journal of Applied Physics, vol. 9,  no. 2, pp. 12-16, 2022. Crossref, https://doi.org/10.14445/23500301/IJAP-V9I2P103

Abstract:

In various articles1 2, 3 , the author developed a mathematical model showing interesting applications in physics. The following article analyzes the coordinates transformation produced by a vectorial pseudo-rotation. The invariant quantities after a pseudo-rotation and the Doppler effect for light are also presented. Still, the paper's main purpose is to deduce the matter wave equation as the natural consequence of intrinsic properties of the "physical world" and its Hnumber representation. Ever since de Broglie formulated his hypothesis, the physics of matter waves was playing an important role in the field of the measurement technique4 . In the last decade, matter waves optics enabled numerous applications ranging from basic science to navigation or detection systems technologies.

Keywords:

VH- numbers representation, Geometrized unit system, Vector pseudo-rotation, Generalized action invariant, Wave associated with a particle, Phase velocity, Group velocity.

References:

[1] Vlad L. Negulescu, “Hyper-Complex Numbers in Physics,” International Journal of Theoretical and Mathematical Physics, vol. 5, no. 2, 2015. Crossref, http://article.sapub.org/10.5923.j.ijtmp.20150502.03.html
[2] Vlad L. Negulescu, “Addition of Velocities, Forces and Powers using Vector H-number Representation,” International Journal of Theoretical and Mathematical Physics, vol. 7, no. 3, 2017. Crossref, http://article.sapub.org/10.5923.j.ijtmp.20170703.03.html
[3] Vlad L. Negulescu, “Motion Analysis of Particles Using the Hyper-Complex Numbers Representation,” Open Access Journal of Mathematical and Theoretical Physics, vol. 2, no. 1, 2019. Crossref, https://medcraveonline.com/OAJMTP/OAJMTP-02- 00047.pdf
[4] Markus Arndt etal., “Focus on Modern Frontiers of Matter Wave Optics and Interferometry,” New Journal of Physics, vol. 14, 2012. Crossref, https://iopscience.iop.org/article/10.1088/1367-2630/14/12/125006
[5] “Geometrized Units System,” [Online]. Available: https://en.wikipedia.org/wiki/Geometrized_unit_system
[6] Vlad L. Negulescu, “The Compressed Particle's Vector and Derived Applications,” SSRG International Journal of Applied Physics, vol. 8, no. 2, pp. 21-29, 2021. [Online]. Available: https://www.internationaljournalssrg.org/IJAP/paper-details?Id=156
[7] Vlad L. Negulescu, “Hypernumbers and their Applications in Mechanics,” Romanian Journal of Physics, vol. 42, no. 3-4, 1997.
[8] E.P. Dolzhenko (originator), “Monogenic Functions,” Encyclopedia of Mathematics, [Online]. Available: http://www.encyclopediaofmath.org/index.php?title=Monogenic_function&oldid=15905
[9] “Holomorphic Function,” [Online]. Available: http://en.wikipedia.org/wiki/Holomorphic_function
[10] “Conformal Map,” [Online]. Available:http://en.wikipedia.org/wiki/Conformal_map
[11] “Radius of Curvature,” [Online]. Available: http://en.wikipedia.org/wiki/Radius_of_curvature_(mathematics)
[12] Wolfgang Rindler, “Introduction to Special Relativity,” Oxford University Press, 1982.
[13] Rapidity, 2014. [Online]. Available: http://en.wikipedia.org/wiki/Rapidity
[14] “Metric Space,” 2014. [Online]. Available: http://en.wikipedia.org/wiki/Metric_space
[15] R.P.Feynman,R. B. Leighton, M. Sands, “The Feynman Lectures on Physics, Mainly Electromagnetism and Matter,” Reading, Mass., Addison-Wesley, 1969.
[16] “Ball in General Metric Spaces,” [Online]. Available: http://en.wikipedia.org/wiki/Ball_(mathematics)
[17] “Plank Constant.” [Online]. Available: http://en.wikipedia.org/wiki/Planck_constant
[18] “Uncertainty Principle,” [Online]. Available: http://en.wikipedia.org/wiki/Uncertainty_principle
[19] “Plane Wave,” [Online]. Available: http://en.wikipedia.org/wiki/Plane_wave
[20] “Matter Wave,” [Online]. Available: http://en.wikipedia.org/wiki/Matter_wave
[21] “Waves,” http://en.wikipedia.org/wiki/Wave#Phase_velocity_and_group_velocity
[22] K.Guerlebeck and W. Sproessig, “Quaternionic and Clifford Calculus for Physicists and Engineers,” Cichester, Wiley, 1997.
[23] R. Adler, M. Bazin, M. Schiffer, “Introduction to General Relativity,” New York, McGraw-Hill, 1965.
[24] R.P. Feynman, R.B. Leighton, M. Sands, “The Feynman Lectures on Physics, Mainly Electromagnetism and Matter,” Reading, Mass., Addison-Wesley, 1969.
[25] Oleg D. Jefimenko, “On the Relativistic Invariance of Maxwell's Equations, Z. Naturforsch,” vol. 54a, pp. 637-644, 1999. [Online]. Available: http://zfn.mpdl.mpg.de/data/Reihe_A/54/ZNA-1999-54a-0637.pdf
[26] “The Universe by Numbers,” [Online]. Available: http://www.physicsoftheuniverse.com/numbers.html.