1996/12/12 by Ali Mostafazadeh, Mostafazadeh, Ali
Physics and Astronomy · #Quantum Mechanics and Applications #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #hep-th #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/9612038
5 pages
arxiv created 1996/12/12 · arxiv updated 2009/11/30
Quantum canonical transformations corresponding to the action of the unitary operator eiε(t)√(f(x))p√(f(x)) is studied. It is shown that for f(x)=x, the effect of this transformation is to rescale the position and momentum operators by eε(t) and e-ε(t), respectively. This transformation is shown to lead to the identification of a previously unknown class of exactly solvable time-dependent harmonic oscillators. It turns out that the Caldirola-Kanai oscillator whose mass is given by m=m0 eγt, belongs to this class. It is also shown that for arbitrary f(x), this canonical transformations map the dynamics of a free particle with constant mass to that of free particle with a position-dependent mass. In other words, they lead to a change of the metric of the space.