Related papers: Canonical transformations in quantum mechanics
Canonical transformations are defined and discussed along with the exponential, the coherent and the ultracoherent vectors. It is shown that the single-mode and the $n$-mode squeezing operators are elements of the group of canonical…
We consider deformations of quantum mechanical operators by using the novel construction of warped convolutions. The deformation enables us to obtain several quantum mechanical effects where electromagnetic and gravitomagnetic fields play a…
Quantum canonical transformations are used to derive the integral representations and Kummer solutions of the confluent hypergeometric and hypergeometric equations. Integral representations of the solutions of the non-periodic three body…
We show that quantum theory allows for transformations of black boxes that cannot be realized by inserting the input black boxes within a circuit in a pre-defined causal order. The simplest example of such a transformation is the classical…
In this work we address the problem of the quantization of a simple harmonic oscillator that is perturbed by a time dependent force. The approach consists of removing the perturbation by a canonical change of coordinates. Since the…
In this paper the theory of time-dependent and time-independent canonical transformations is considered from a geometric perspective. Both the geometric formalism and the coordinate based approach are described in detail. In particular,…
In a previous article [H. Bergeron, J. Math. Phys. 42, 3983 (2001)], we presented a method to obtain a continuous transition from classical to quantum mechanics starting from the usual phase space formulation of classical mechanics. This…
In this article we review some results obtained from a generalization of quantum mechanics obtained from modification of the canonical commutation relation $[q,p]={\rm i}\hbar$. We present some new results concerning relativistic…
Familiar formulations of classical and quantum mechanics are shown to follow from a general theory of mechanics based on pure states with an intrinsic probability structure. This theory is developed to the stage where theorems from quantum…
We show that the dynamics of a quantum system can be represented by the dynamics of an underlying classical systems obeying the Hamilton equations of motion. This is achieved by transforming the phase space of dimension $2n$ into a Hilbert…
Deformation quantization (sometimes called phase-space quantization) is a formulation of quantum mechanics that is not usually taught to undergraduates. It is formally quite similar to classical mechanics: ordinary functions on phase space…
We discuss the deformation quantization approach for the teaching of quantum mechanics. This approach has certain conceptual advantages which make its consideration worthwhile. In particular, it sheds new light on the relation between…
A new formulation of potential scattering in quantum mechanics is developed using a close structural analogy between partial waves and the classical dynamics of many non-interacting fields. Using a canonical formalism we find non-linear…
In classical theory, the physical systems are elucidated through the concepts of particles and waves, which aim to describe the reality of the physical system with certainty. In this framework, particles are mathematically represented by…
After revealing difficulties of the standard time-dependent perturbation theory in quantum mechanics mainly from the viewpoint of practical calculation, we propose a new quasi-canonical perturbation theory. In the new theory, the dynamics…
Quantum dynamics can be regarded as a generalization of classical finite-state dynamics. This is a familiar viewpoint for workers in quantum computation, which encompasses classical computation as a special case. Here this viewpoint is…
The measure of distinguishability between two neighboring preparations of a physical system by a measurement apparatus naturally defines the line element of the preparation space of the system. We point out that quantum mechanics can be…
We show how quantum mechanics can be understood as a space-time theory provided that its spatial continuum is modelled by a variable real number (qrumber) continuum. Such a continuum can be constructed using only standard Hilbert space…
On classical phase spaces admitting just one complex-differentiable structure, there is no indeterminacy in the choice of the creation operators that create quanta out of a given vacuum. In these cases the notion of a quantum is universal,…
A novel canonical transformation is offered as the mean for studying properties of a system of strongly correlated electrons. As an example of the utility of the transformation, it is used to demonstrate the existence of a quantum phase…