Quantum bouncer with quadratic dissipation
Gabriel González
NanoScience Technology Center, University of Central Florida, Orlando, FL 32826, USA, Department of Physics, University of Central Florida, Orlando, FL 32816–2385, USA, e–mail: ggonzalez@physics. ucf.edu
Recibido el 1 de octubre de 2007
Aceptado el 28 de enero de 2008
Abstract
The energy loss due to a quadratic velocity–dependent force on a quantum particle bouncing off a perfectly reflecting surface is obtained for a full cycle of motion. We approach this problem by means of a new, effective, phenomenological Hamiltonian which corresponds to the actual energy of the system and obtain the correction to the eigenvalues of the energy in first–order quantum perturbation theory for the case of weak dissipation.
Keywords: Quantum bouncer; dissipative systems; canonical quantization.
Resumen
La pérdida de energía debido a una fuerza proporcional al cuadrado de la velocidad se obtiene para el movimiento de una partícula en el campo gravitacional uniforme. Se propone un nuevo Hamiltoniano efectivo para obtener las correciones a los eigenvalores, utilizando la teoría de perturbaciones para el caso de disipacion débil.
Descriptores: Rebotador cuántico; sistemas disipativos; cuantización canónica.
PACS: 03.65.–w; 03.65.Sq
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