PHAS Colloquia

A non-relativistic approach to relativistic quantum mechanics

by Luis A. Poveda (Technological Center of Minas Gerais, Brazil)

Tuesday, 7 September 2021 from to (America/Chicago)
Speaker: Dr. Luis Poveda (Physics, Technological Center of Minas Gerais, Belo Horizonte, Brazil)

Title: A non-relativistic approach to relativistic quantum mechanics

Abstract: In the formulation of a relativistic quantum mechanics, a mathematical difficulty arises when the classical quantities E and p are substituted by their corresponding quantum operators, in the classical relativistic energy-momentum relation: E = sqrt(m^2*c^2 + c^2 p·p). The resulting mathematical object, in the position representation, involves the square-root of a differential operator, whose definition only makes sense in the momentum space. One alternative to avoid this cumbersome square-root operator was followed by Oskar Klein and Walter Gordon [1], who applied the first quantization to the norm squared of the relativistic four-momentum, leading to a second-order equation in both time and space. In this talk, an ongoing effort to make treatable the square-root operator, within a relativistic formulation of quantum mechanics, will be presented [2-5]. The main advantage of this formalism is that, for all practical purposes, the resolution of a Schr ̈odinger-like equation is required [2-5]. Exact and approximate methods will be discussed, as well as some application in obtaining a generalization of well known non-relativistic solutions into the relativistic domain.

[1] O. Klein, Z. Phys., 37, 895, 1926; W. Gordon, Z. Phys. , 40, 1926, 117, 1926.
[2] L. Grave de Peralta, “Did Schr ̈odinger have other options?” Eur. J. Phys. 41, 065404, 2020.
[3] L. A. Poveda, L. Grave de Peralta, and A. Ruiz-Columbi ́e. “Relativistic correction to the Di ́osi-Penrose model” arXiv:2103.00994, 2021.
[4] L. Grave de Peralta, L. A. Poveda, and Bill Poirier, “Making relativistic quantum mechanics simple”, Eur. J. Phys. 42, 055404, 2021.
[5] L. A. Poveda, L. Grave de Peralta, J. Pittman, and B. Poirier.
“A non-relativistic approach to relativistic quantum mechanics: the case of the harmonic oscillator” (to be published).

About the speaker: Dr. Luis Poveda is associated professor at the Physics Department of the Technological Center of Minas Gerais, in Belo Horizonte, Brazil. He received the PhD. in 2007, from the Coimbra University, Portugal, and the B.S. degree in Physics in 1991, from the Oriente University, Cuba. His research interest includes: electronic structure calculations, modeling of potential energy surfaces for molecular dynamics, calculation of scattering cross sections of low-energy positrons in atoms and molecules, and very recently Dr. Poveda has been working on relativistic quantum mechanics, in a fruitful collaboration with researchers from the Texas Tech University.


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Meeting ID: 995 291 7599
Passcode: PHAS


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Organised by Luis Grave-De-Peralta/ QIS