相关论文: Quantum mechanics in phase space: The Schr\"odinge…

We develop the quantum field theory of fermion mixing in curved spacetime and discuss the role of unitarily inequivalent representations in the particle interpretation of the theory. We derive general oscillation formulae and apply them to…

On using the known equivalence between the presence of a position-dependent mass (PDM) in the Schr\"odinger equation and a deformation of the canonical commutation relations, a method based on deformed shape invariance has recently been…

We deform the interaction between nonrelativistic point particles on a plane and a Chern-Simons field to obtain an action invariant with respect to time-dependent area-preserving diffeomorphisms. The deformed and undeformed Lagrangians are…

We show that the quantum wavefunction, interpreted as the probability density of finding a single non-localized quantum particle, which evolves according to classical laws of motion, is an intermediate description of a material quantum…

The phase space of quantum mechanics can be viewed as the complex projective space endowed with a Kaehlerian structure given by the Fubini-Study metric and an associated symplectic form. We can then interpret the Schrodinger equation as…

The primary motivation for Moyal's approach to quantum mechanics was to develop a phase space formalism for quantum phenomena by generalising the techniques of classical probability theory. To this end, Moyal introduced a quantum version of…

We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…

De Broglie and Bohm formulated a causal quantum mechanics with a phase space density whose integral over momentum reproduces the position probability density of usual statistical quantum theory. We propose a causal quantum theory with a…

We investigate within the formalism of Symplectic Quantum Mechanics a two-dimensional non-relativistic strong interacting system that represents the bound heavy quark-antiquark state, where it was considered a linear potential in the…

In quantum statistical mechanics, Moyal's equation governs the time evolution of Wigner functions and of more general Weyl symbols that represent the density matrix of arbitrary mixed states. A formal solution to Moyal's equation is given…

A theory of nonunitary-invertible as well as unitary canonical transformations is formulated in the context of Weyl's phase space representations. Exact solutions of the transformation kernels and the phase space propagators are given for…

This paper investigates quantum simulation algorithms for the Liouville equation in geometrical optics with partial transmission and reflection at sharp interfaces, based on the Schr\"odingerization method. By means of a warped phase…

It is shown that quantum mechanics on noncommutative (NC) spaces can be obtained by canonical quantization of some underlying constrained systems. Noncommutative geometry arises after taking into account the second class constraints…

The wave equation in quantum mechanics and its general solution in the phase space are obtained.

An elementary introduction is provided to the phase space quantization method of Moyal and Wigner. We generalize the method so that it applies to 2-dimensional surfaces, where it has an interesting connection with quantum holography. In the…

Precanonical quantization is based on a generalization of the Hamiltonian formalism to field theory, the so-called De Donder-Weyl (DW) theory, which does not require a spacetime splitting and treats the space-time variables on an equal…

States of nonlinear quantum oscillators (f-oscillators) are considered in the Weyl-Wigner-Moyal representation and the tomographic probability representation, where the states are described by standard probability distributions instead of…

For a general class of unitary quantum maps, whose underlying classical phase space is divided into several invariant domains of positive measure, we establish analogues of Weyl's law for the distribution of eigenphases. If the map has one…

The full spectrum and eigenfunctions of the quantum version of a nonlinear oscillator defined on an N-dimensional space with nonconstant curvature are rigorously found. Since the underlying curved space generates a position-dependent…

Non-relativistic quantum mechanics is shown to emerge from classical mechanics through the requirement of a relativity principle based on special transformations acting on position and momentum uncertainties. These transformations keep the…