[hal-01077079] Time dependent quaritum harmonic oscillator subject to a sudden change of mass continuous solution

We show that a harmonic oscillator subject to a sudden change of mas s produces squeezed states Our study is based on an approximate analytic solution to the time-dependent harmonic oscillator equation with a subperiod function parameter This continuous treatment differs from former studies that involve the matching of two time-independent solutions at the discontinuity This formalism requires an ad hoc transformation of the original differential equation and isalso applicable for rapid although not necessarily instantaneous mass variations Keywords Solutions in closed form quantum mechanics exact invariants Mostramos que un oscilador armónico sujeto a un cambio repentino de masa produce estados comprimidos Nuestro estudio está basado en una solución analítica aproximada para el oscilador armónico dependiente del tiempo El tratamiento continuo que estudiamos difiere de estudios anteriores en los cuales se igualan las soluciones en la discontinuidad Nuestro formalismo requiere una transformación ad hoc de la ecuación diferencial original y es aplicable también para variaciones de masa rápidas no solo instantáneas Descriptores Soluciones analíticas mecánica cuántica invariantes exactos PACS 0365La 0365Ge 0230Ik 1 Introduction ing another transforrnation that produces a monotonic time-dependent parameter The transformed equation can then be sol ved with the continuum approach leading to squeezing of the momentum variables at certain times An interesting ad-vantage of this method is that the change of mass need not be a step function in the strict mathematical sense The require-ment which is physically more plausible is that the change in mass should take place in a time span much shorter than the characteristic period of the oscillator The plan of the manuscript is the following in Seco 2 we write the quadratic and linear invariants for a time-dependent mass and exhibit their relation with the Hamiltonian In Seco 3 we discuss two transforrnations that translate the clas-sical time-dependent mass equation into the time dependent trequency problem The analytic solution for a rapid varia-tion of the time dependent mass using the appropriate trans-formation is then presented In Seco 4 we exhibit how a sudden change of mas s in the quantum oscillator produces squeezing Section 5 is left for conclusions 2 Time dependent mass



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