2 research outputs found
Harmonic states for the free particle
Different families of states, which are solutions of the time-dependent free
Schr\"odinger equation, are imported from the harmonic oscillator using the
Quantum Arnold Transformation introduced in a previous paper. 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.Comment: 21 pages, 3 figures. Title changed, content added, references adde