Authors:
Guerrero, J (Guerrero, J.)1,2; Lopez-Ruiz, FF (Lopez-Ruiz, F. F.)2; Aldaya, V (Aldaya, V.)2; Cossio, F (Cossio, F.)2
Abstract:
Different families of states, which are solutions of the time-dependent free Schrodinger equation, are imported from the harmonic oscillator using the quantum Arnold transformation introduced in Aldaya et al (2011 J. Phys. A: Math. Theor. 44 065302). Among them, infinite series of states are given that are normalizable, expand the whole space of solutions, are spatially multi-localized and are eigenstates of a suitably defined number operator. Associated with these states new sets of coherent and squeezed states for the free particle are defined representing traveling, squeezed, multi-localized wave packets. These states are also constructed in higher dimensions, leading to the quantum mechanical version of the Hermite-Gauss and Laguerre-Gauss states of paraxial wave optics. Some applications of these new families of states and procedures to experimentally realize and manipulate them are outlined.
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