The aim of this book is to give a rigorous and complete treatment of various topics from
harmonic analysis with a strong emphasis on symplectic invariance properties, which are …

This paper develops an alternative formulation of quantum mechanics known as the phase
space quantum mechanics or deformation quantization. It is shown that the quantization …

Symplectic quantum mechanics (SMQ) makes possible to derive the Wigner function without
the use of the Liouville–von Neumann equation. In this formulation of the quantum theory the …

This paper presents the general theory of canonical transformations of coordinates in
quantum mechanics. First, the theory is developed in the formalism of phase space quantum …

The relevance of modulation spaces for deformation quantization, Landau--Weyl
quantization and noncommutative quantum mechanics became clear in recent work. We …

The usual Weyl calculus is intimately associated with the choice of the standard symplectic
structure on Rn⊕ Rn. In this paper we will show that the replacement of this structure by an …

It is well known for physicists that in order to describe dynamical systems of finite number of
degrees of freedom in the macro-and micro-scale, classical and quantum mechanics …

We show that the deformation quantization of noncommutative quantum mechanics
previously considered by Dias and Prata [“Weyl–Wigner formulation of noncommutative …

For a general self-adjoint Hamiltonian operator $ H_0 $ on the Hilbert space $ L^ 2 (R^ d) $,
we determine the set of all self-adjoint Hamiltonians $ H $ on $ L^ 2 (R^ d) $ that …

We propose a dissipative scheme to prepare maximally entangled steady states in cavity
QED setup, consisting of two two-level atoms interacting with the two counter-propagating …