Weyl-Wigner formalism for rotation-angle and angular-momentum variables in quantum mechanics

Abstract

A comprehensive study is presented on the Weyl-Wigner formalism for rotation-angle and angularmomentum variables: the elements of kinematics are extended, the elements of dynamics are established, and the implications of rotational perodicity and angular-momentum quantization are investigated. Particular attention is paid to discreteness, and two of its consequences are emphasized: the importance of evenness and oddness, and the need to use two difference operators in a discrete domain, whereas one difFerential operator suSces in a continuous domain. These consequences are shown to strongly distinguish the Weyl-signer formalism for rotation-angle and angular-momentum

Wigner representation of the rotational dynamics of rigid tops

“…A variety of ways to extend the original Wigner quantization ansatz to the case of rotational dynamics were suggested and analyzed [27][28][29][30][31][32][33][34][35][36][37][38][39], but only a few of them are applicable to unrestricted rotations of 3-dimensional bodies. The early solutions of Refs.…”

The Number-Phase Wigner Function in the Extended Fock Space

“…Following Bizarro [8] and Vaccaro [5], we introduce the six conditions to determine the Wigner operatorŴ .…”

“…The correct integral expressions can be obtained by making use of the phase states. Then, it becomes clear thatŜ 1 andŜ 2 cannot be defined uniquely, although Bizarro [8] states thatŜ 2 is determined uniquely by six "natural" conditions. In fact, there are infinite possibilities of defining number-phase Wigner operators satisfying these conditions.…”

“…In particular, Bizarro [8] derived the function starting from six "natural" conditions, which constitute an appropriate way for constructing the function.…”

“…Several authors [6,7,8,9] have studied the rotational Wigner function for rotation angle and angular momentum. In particular, Bizarro [8] derived the function starting from six "natural" conditions, which constitute an appropriate way for constructing the function.…”