Méndez-Rodríguez, Rubén

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    On the formalism of quantum mechanics constructed with the dispersion relation of deformed special relativity
    (2011) Méndez-Rodríguez, Rubén; Marrero-Soto, Pablo J.; College of Arts and Science - Science; Roura-Davila, Erick; Ramírez-Vargas, Juan Eduardo; Department of Physics; Jiménez, Manuel
    Over the last ten years there has been a significant effort to develop Deformed Special Relativity (DSR). This theory has two observer invariant scales: the speed of light,(c), and the Planck energy,(Ep). It is argued by F. Girelli, E.R. Livine, and D. Oriti that this type of theory is an effective flat limit of quantum gravity. The idea behind the formulation of such theories is that at energies comparable to EP the energy momentum dispersion relation E2 = p2c2 + m2c4 must be modified by quantum gravitational effects. As shown by Amelino-Camelia and Piran the dispersion relation will have the general form: E2 = p2c2 + m2c4 + λE3 + ··· where λ is of the order of Planck length (inverse of Ep) This modification of the dispersion relation induces changes in the structure of the relativistic wave equations and the Schrödinger equation. The main goal of this project is to determine the form of the DSR-modified Schrödinger equation and to explicitly calculate the DSR corrections to its solutions for d = 1 and d = 3 problems. The Free Particle, the Harmonic Oscillator, and the Hydrogen Atom were studied. The study also includes applications of the Lagrangian formalism and the effects of local gauge transformations on the Lagrangian of the theory.