A Bohmian total potential view to quantum effects. II: decay of temporarily trapped states
Formation, persistence and decay of temporarily trapped states, the time-dependent generalization of resonances, are analysed within the framework of Bohmian Mechanics. More specifically, the so-called Bohm’s total potential, the sum of classical plus Bohm’s quantum potential, is used. It is found that both formation and decay are triggered by the frequency in the oscillations of the total potential. These oscillations have been studied at the specific locations where the classical potential displays maxima, i.e. the ‘walls’ temporarily capturing the system’s density. Our main result is that the total potential oscillation frequency is solely dependent on the steepness of the classical potential ramp and, surprisingly, independent of the classical barrier height and width, well depth and width, collision energy or wavepacket width.
KeywordsBohmian mechanics Resonances Quantum dynamics
The authors are among several generations of former students of Professor Santiago Olivella. It has been a true honor to have learned from the inspiring environment and mastership provided by him, along nearly four decades, so that dedicating the present work to him is just the minimum we could do as acknowledgement. Thanks a lot, Santiago!. The authors are grateful for the financial support provided by the Spanish Ministerio de Ciencia y Tecnología, DGI project CTQ2005-01117/BQU, and in part by the Generalitat de Catalunya projects 2005SGR-00111 and 2005SGR-00175, which is fully acknowledged.
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