TITLE:
The Wigner Quasiprobability and Its Integration over the Radius for Coherent States
AUTHORS:
Alfred Wünsche
KEYWORDS:
Glauber-Sudarshan Quasiprobability, Husimi-Kano Quasiprobability, Operator Ordering, Coherent States, Even and Odd Coherent States, Convolution, Heitler Uncertainty Relation, Convolutions
JOURNAL NAME:
Journal of Modern Physics,
Vol.17 No.10,
October
28,
2026
ABSTRACT: The first part is a systematical representation of the Wigner quasiprobability in representations by canonical variables and pairs of complex conjugate variables with particular attention to the reconstruction of the density operator from the Wigner quasiprobability to show their equivalence. All formulae are derived from basic postulates of quantum mechanics. Problems of operator orderings are touched. The second part considers the integration over the amplitude in the Wigner quasiprobability and its specialization for coherent states and for even and odd coherent states and provides phase distributions which are presented in graphics that are new in their kind. It is demonstrated that the Heitler number phase uncertainty relation is incorrect. The problem of the transition from quantum to classical distribution functions by
ℏ→0
is discussed with the conjecture that the inertial point of the distributions plays a basic role.