Abstract
A Schrodinger-like equation for a single free quantum particle is presented. It is argued that this equation can be considered a natural relativistic extension of the Schrodinger equation for energies smaller than the energy associated to the particle’s mass. Some basic properties of this equation: Galilean invariance, probability density, and relation to the Klein-Gordon equation are discussed. The scholastic value of the proposed Grave de Peralta equation is illustrated by finding precise quasi-relativistic solutions for the infinite rectangular well and the quantum rotor problems. Consequences of the non-linearity of the proposed equation for the quantum superposition principle are discussed.
Highlights
Introduction1925, the Schrödinger equation has been often used for introducing the fundamentals of quantum mechanics [1] [2] [3] [4] [5]
Since the discovery of the quantum wave mechanics by Erwin Schrödinger in1925, the Schrödinger equation has been often used for introducing the fundamentals of quantum mechanics [1] [2] [3] [4] [5]
Explicit quasi-relativistic solutions of Equation (3) can be found with no more complexity than in standard textbook examples of solvable Schrödinger equation problems [1] [2] [3] [4] [5]. This illustrates the scholastic value of the Grave de Peralta equation for introducing learners to the intricacies of the fully relativistic quantum mechanics and quantum fields theory
Summary
1925, the Schrödinger equation has been often used for introducing the fundamentals of quantum mechanics [1] [2] [3] [4] [5]. The Galilean invariance of Equation (1) means that two such observers will only agree in the adequacy of Equation (1) for describing the movement of a massive free quantum particle when the relative speed between the observers (Vo) is much smaller than the speed of the light in the vacuum (c) This is not a terrible limitation of the Schrödinger equation because up to today humans have been only able to travel at speeds much smaller than c. Explicit quasi-relativistic solutions of Equation (3) can be found with no more complexity than in standard textbook examples of solvable Schrödinger equation problems [1] [2] [3] [4] [5] This illustrates the scholastic value of the Grave de Peralta equation for introducing learners to the intricacies of the fully relativistic quantum mechanics and quantum fields theory.
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