TY - JOUR
T1 - A non-relativistic approach to relativistic quantum mechanics: the case of the harmonic oscillator
T2 - The Case of the Harmonic Oscillator
AU - Grave De Peralta, Luis
AU - Poirier, Lionel
AU - Poveda, Luis
AU - Pittman, Klay
AU - Pittman, Jacob
N1 - Funding Information:
Authors Pittman and Poirier acknowledge support from a grant from the Robert A. Welch Foundation (D-1523). We also wish to thank the anonymous referees, in particular for calling to our attention previous works dedicated to solutions of the spinless Salpeter equation.
Funding Information:
Partial financial support was received from Robert A. Welch Foundation, Grant D-1523.
Publisher Copyright:
© 2022, The Author(s).
PY - 2022/2
Y1 - 2022/2
N2 - A recently proposed approach to relativistic quantum mechanics (Grave de Peralta, Poveda, Poirier in Eur J Phys 42:055404, 2021) is applied to the problem of a particle in a quadratic potential. The methods, both exact and approximate, allow one to obtain eigenstate energy levels and wavefunctions, using conventional numerical eigensolvers applied to Schrödinger-like equations. Results are obtained over a nine-order-of-magnitude variation of system parameters, ranging from the non-relativistic to the ultrarelativistic limits. Various trends are analyzed and discussed—some of which might have been easily predicted, others which may be a bit more surprising.
AB - A recently proposed approach to relativistic quantum mechanics (Grave de Peralta, Poveda, Poirier in Eur J Phys 42:055404, 2021) is applied to the problem of a particle in a quadratic potential. The methods, both exact and approximate, allow one to obtain eigenstate energy levels and wavefunctions, using conventional numerical eigensolvers applied to Schrödinger-like equations. Results are obtained over a nine-order-of-magnitude variation of system parameters, ranging from the non-relativistic to the ultrarelativistic limits. Various trends are analyzed and discussed—some of which might have been easily predicted, others which may be a bit more surprising.
KW - Harmonic oscillator
KW - Klein–Gordon equation
KW - Schrödinger equation
KW - Spinless Salpeter equation
KW - WKB approximation
UR - http://www.scopus.com/inward/record.url?scp=85124984614&partnerID=8YFLogxK
U2 - 10.1007/s10701-022-00541-5
DO - 10.1007/s10701-022-00541-5
M3 - Article
SN - 0015-9018
VL - 52
JO - Foundations of Physics
JF - Foundations of Physics
IS - 1
M1 - 29
ER -