We analyze the time-dependent solutions of the pseudo-differential L´evy– Schr¨odinger wave equation in the free case, and compare them with the associated L´evy processes. We list the principal laws used to describe the time evolutions of both the L´evy process densities and the L´evy–Schr¨odinger wave packets. To have self-adjoint generators and unitary evolutions we will consider only absolutely continuous, infinitely divisible L´evy noises with laws symmetric under change of sign of the independent variable. We then show several examples of the characteristic behavior of the L´evy–Schr¨odinger wave packets, and in particular of the multimodality arising in their evolutions: a feature at variance with the typical diffusive unimodality of both the corresponding L´evy process densities and usual Schr¨odinger wavefunctions.
Lévy-Schrödinger wave packets
CUFARO PETRONI, Nicola
2011-01-01
Abstract
We analyze the time-dependent solutions of the pseudo-differential L´evy– Schr¨odinger wave equation in the free case, and compare them with the associated L´evy processes. We list the principal laws used to describe the time evolutions of both the L´evy process densities and the L´evy–Schr¨odinger wave packets. To have self-adjoint generators and unitary evolutions we will consider only absolutely continuous, infinitely divisible L´evy noises with laws symmetric under change of sign of the independent variable. We then show several examples of the characteristic behavior of the L´evy–Schr¨odinger wave packets, and in particular of the multimodality arising in their evolutions: a feature at variance with the typical diffusive unimodality of both the corresponding L´evy process densities and usual Schr¨odinger wavefunctions.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
