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Introducing Relativity in Quantum Mechanics

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Relativistic and Non-Relativistic Quantum Mechanics

Abstract

In 1905, Albert Einstein discovered the special theory of relativity. In 1925, Schrödinger knew that any foundational law of physics should be Lorentz covariant. Schrödinger knew that the equation that is named after him today, was not Lorentz’s covariant, but Galileo’s invariant. For practical reasons, he chose to publish the equation that carries his name today. He chose to publish this instead of a Lorentz covariant equation that is known as the Klein-Gordon equation in modern times. The reason for Schrödinger’s decision was because of the evidence that the Klein-Gordon equation for a free particle has solutions with negative kinetic energy. On the contrary, the kinetic energy of classical particles is always positive. In this chapter, this book diverges from a traditional introduction to quantum mechanics. The first proposed ideas of relativistic quantum mechanics are introduced for a background sense of what this book wants to ultimately pursue. This includes the introduction of the Schrödinger-like PPGP equation and its use to solve simple one-dimensional problems.

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Correspondence to Luis Grave de Peralta .

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Grave de Peralta, L., Fernández Lozada, M., Farooq, H., Eichman, G., Singh, A., Prime, G. (2023). Introducing Relativity in Quantum Mechanics. In: Relativistic and Non-Relativistic Quantum Mechanics. Undergraduate Lecture Notes in Physics. Springer, Cham. https://doi.org/10.1007/978-3-031-37073-1_3

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