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Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento B

Space- and time-dependentN-particle distribution functions

C. Syros

Published Nov 1, 1976• 1 citation
Publisher
DOI
10.1007/bf02749422

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We used the concept of quasienergy of the quantum state of a particle in a time-oscillating parabolic potential to find the particle’s distribution function thermalized by collisions with surrounding gas molecules. When the collision frequency is much smaller than the inverse period of the potential this distribution has a Boltzmannian form with respect to quasienergy. Using quasienergy distribution and exact wave functions we found the Wigner function of the particle and its classical time-dependent space-velocity distribution [eq. (18)]. To illustrate the applicability of the quasienergy approach we compare this result with the exact solution of the Fokker–Planck equation, which gives a model description at arbitrary collision frequency.
In this manuscript, I speculated that the energy density distributions along space and time in a quantum system are uniform. Thus, the complementary energy contributions are added to the classical solutions of the 1D particle in a box problem, making the energy density a complex distribution function over space and time. Then the concept is extended to the free rotation problem with a Hamiltonian slightly different than the classical Schrödinger equation. The picturized energy distribution functions and associated time evolution are described in movies for comparison between example classical wave functions and the energy density function.