Direct relativistic extension of the Schrodinger equation
POSTER
Abstract
Recent results obtained by solving the following relativistic equation for a particle with mass m and spin-0 [1-5]:
ih ∂Ψ/∂t = -h2/[(γv+1)m] ▽2Ψ + V, γv = (1-v2/c2)-1/2 (1)
are discussed. In Eq. (1), h is the reduced Plank constant, and γv depends on the ratio between the particle speed (v) and the speed of the light in the vacuum (c) . Clearly, Eq. (1) coincides with the Schrodinger equation when v2 << c2. Due to the formal similarity between Eq. (1) and the Schrodinger equation, Eq. (1) can be solved following the same procedures used for solving the Schrodinger equation [1-5]; therefore, Eq. (1) provides a pedagogical approach for introducing the consequences for Quantum Mechanics of the principal ideas of Special Theory of Relativity. Moreover, Eq. (1) allows simpler approaches for a relativistic description of the quantum states of a particle [1-5]. The existing relationship between Eq. (1) and the Dirac, and Klein-Gordon equations are also discussed.
1. L. Grave de Peralta, European Journal of Physics, 41, 065404 (2020).
2. L. Grave de Peralta, Scientific Reports 10, 14925 (2020).
3. L. Grave de Peralta, Results in Physics 18, 103318 (2020).
4. L. Grave de Peralta, Journal of Modern Physics 11, 788 (2020).
5. L. Grave de Peralta, Journal of Modern Physics 11, 196 (2020).
ih ∂Ψ/∂t = -h2/[(γv+1)m] ▽2Ψ + V, γv = (1-v2/c2)-1/2 (1)
are discussed. In Eq. (1), h is the reduced Plank constant, and γv depends on the ratio between the particle speed (v) and the speed of the light in the vacuum (c) . Clearly, Eq. (1) coincides with the Schrodinger equation when v2 << c2. Due to the formal similarity between Eq. (1) and the Schrodinger equation, Eq. (1) can be solved following the same procedures used for solving the Schrodinger equation [1-5]; therefore, Eq. (1) provides a pedagogical approach for introducing the consequences for Quantum Mechanics of the principal ideas of Special Theory of Relativity. Moreover, Eq. (1) allows simpler approaches for a relativistic description of the quantum states of a particle [1-5]. The existing relationship between Eq. (1) and the Dirac, and Klein-Gordon equations are also discussed.
1. L. Grave de Peralta, European Journal of Physics, 41, 065404 (2020).
2. L. Grave de Peralta, Scientific Reports 10, 14925 (2020).
3. L. Grave de Peralta, Results in Physics 18, 103318 (2020).
4. L. Grave de Peralta, Journal of Modern Physics 11, 788 (2020).
5. L. Grave de Peralta, Journal of Modern Physics 11, 196 (2020).
Presenters
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Luis Grave de Peralta
Texas Tech Univ
Authors
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Luis Grave de Peralta
Texas Tech Univ
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Bill Poirier
Department of Chemistry and Biochemistry and Department of Physics and Astronomy Texas Tech University
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Luis A. Poveda
Centro Federal de Educação Tecnológica de Minas Gerais, Belo Horizonte, 30421-169, MG Brasil