TY - JOUR

T1 - Comparing Wigner, Husimi and Bohmian distributions: which one is a true probability distribution in phase space?

AU - Colomés, E.

AU - Zhan, Z.

AU - Oriols, X.

PY - 2015/12/23

Y1 - 2015/12/23

N2 - © 2015, Springer Science+Business Media New York. The Wigner distribution function is a quasi-probability distribution. When properly integrated, it provides the correct charge and current densities, but it gives negative probabilities in some points and regions of the phase space. Alternatively, the Husimi distribution function is positive-defined everywhere, but it does not provide the correct charge and current densities. The origin of all these difficulties is the attempt to construct a phase space within a quantum theory that does not allow well-defined (i.e. simultaneous) values of the position and momentum of an electron. In contrast, within the (de Broglie–Bohm) Bohmian theory of quantum mechanics, an electron has well-defined position and momentum. Therefore, such theory provides a natural definition of the phase space probability distribution and by construction, it is positive-defined and it exactly reproduces the charge and current densities. The Bohmian distribution function has many potentialities for quantum problems, in general, and for quantum transport, in particular, that remains unexplored.

AB - © 2015, Springer Science+Business Media New York. The Wigner distribution function is a quasi-probability distribution. When properly integrated, it provides the correct charge and current densities, but it gives negative probabilities in some points and regions of the phase space. Alternatively, the Husimi distribution function is positive-defined everywhere, but it does not provide the correct charge and current densities. The origin of all these difficulties is the attempt to construct a phase space within a quantum theory that does not allow well-defined (i.e. simultaneous) values of the position and momentum of an electron. In contrast, within the (de Broglie–Bohm) Bohmian theory of quantum mechanics, an electron has well-defined position and momentum. Therefore, such theory provides a natural definition of the phase space probability distribution and by construction, it is positive-defined and it exactly reproduces the charge and current densities. The Bohmian distribution function has many potentialities for quantum problems, in general, and for quantum transport, in particular, that remains unexplored.

KW - Bohmian distribution

KW - Husimi distribution

KW - Phase space

KW - Wigner distribution

U2 - 10.1007/s10825-015-0737-6

DO - 10.1007/s10825-015-0737-6

M3 - Article

VL - 14

SP - 894

EP - 906

JO - Journal of Computational Electronics

JF - Journal of Computational Electronics

SN - 1569-8025

IS - 4

ER -