• Media type: E-Article
  • Title: Rapidly decaying Wigner functions are Schwartz functions
  • Contributor: Hernández, Felipe; Riedel, C. Jess
  • Published: AIP Publishing, 2022
  • Published in: Journal of Mathematical Physics, 63 (2022) 2
  • Language: English
  • DOI: 10.1063/5.0049581
  • ISSN: 0022-2488; 1089-7658
  • Keywords: Mathematical Physics ; Statistical and Nonlinear Physics
  • Origination:
  • Footnote:
  • Description: We show that if the Wigner function of a (possibly mixed) quantum state decays toward infinity faster than any polynomial in the phase space variables x and p, then so do all its derivatives, i.e., it is a Schwartz function on phase space. This is equivalent to the condition that the Husimi function is a Schwartz function, that the quantum state is a Schwartz operator in the sense of Keyl et al. [Rev. Math. Phys. 28(03), 1630001 (2016)], and, in the case of a pure state, that the wavefunction is a Schwartz function on configuration space. We discuss the interpretation of this constraint on Wigner functions and provide explicit bounds on Schwartz seminorms.