2022
DOI: 10.1007/s10701-022-00541-5
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A Non-relativistic Approach to Relativistic Quantum Mechanics: The Case of the Harmonic Oscillator

Abstract: 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 ultrarela… Show more

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Cited by 9 publications
(14 citation statements)
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“…Anyway, after substituting the operator γ by the parameter γ, we can use Equation (2) for rewriting Equation (11) as Equation (1). The case μ = μ + = (1 + γ) m/2 > 0 have been intensively studied before [4] ( )…”
Section: The Ggp Equationsmentioning
confidence: 99%
See 4 more Smart Citations
“…Anyway, after substituting the operator γ by the parameter γ, we can use Equation (2) for rewriting Equation (11) as Equation (1). The case μ = μ + = (1 + γ) m/2 > 0 have been intensively studied before [4] ( )…”
Section: The Ggp Equationsmentioning
confidence: 99%
“…Solving Equation (13) gives the energies E K V + + ′ = + , with K + > 0, and the wavefunctions Ψ + corresponding to a relativistic spin-0 particle of mass m, which is moving in the scalar potential V [4] [5] [8] [9] [10] [14] [15]. We will focus our attention now in the case μ = μ -= -(1+ γ)m/2 < 0:…”
Section: The Ggp Equationsmentioning
confidence: 99%
See 3 more Smart Citations