Related papers: Quantum Canonical Transformations: Physical Equiva…
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…
A two-dimensional quantum system with anyonic excitations can be considered as a quantum computer. Unitary transformations can be performed by moving the excitations around each other. Measurements can be performed by joining excitations in…
This paper is a generalization of previous work on the use of classical canonical transformations to evaluate Hamiltonian path integrals for quantum mechanical systems. Relevant aspects of the Hamiltonian path integral and its measure are…
The landscape of causal relations that can hold among a set of systems in quantum theory is richer than in classical physics. In particular, a pair of time-ordered systems can be related as cause and effect or as the effects of a common…
It is shown that the recently proposed quantum analogue of classical energy equipartition theorem for two paradigmatic, exactly solved models (i.e., a free Brownian particle and a dissipative harmonic oscillator) also holds true for all…
In this tenth paper of the series we aim at showing that our formalism, using the Wigner-Moyal Infinitesimal Transformation together with classical mechanics, endows us with the ways to quantize a system in any coordinate representation we…
It is shown that quantum mechanics is a plausible statistical description of an ontology described by classical electrodynamics. The reason that no contradiction arises with various no-go theorems regarding the compatibility of QM with a…
We introduce the first complete equational theory for quantum circuits. More precisely, we introduce a set of circuit equations that we prove to be sound and complete: two circuits represent the same unitary map if and only if they can be…
Incompatibility between conjugate variables and complementary pictures comes in two kinds, exclusive of one another. The first kind is unconditional, and the second conditional on quantum's indivisibility. We employ this distinction to…
A two-time quantum theory of a system of two particles with the direct electromagnetic interaction based on a quantum version of the action principle is considered. An analog of Schrodinger equation for the system is obtained.
In the context of a physical theory, two devices, A and B, described by the theory are called incompatible if the theory does not allow the existence of a third device C that would have both A and B as its components. Incompatibility is a…
A new approach to quantum mechanics based on independence of the Continuum Hypothesis is proposed. In one-dimensional case, it is shown that the properties of the set of intermediate cardinality coincide with quantum phenomenology.
A two boundary quantum mechanics without time ordered causal structure is advocated as consistent theory. The apparent causal structure of usual "near future" macroscopic phenomena is attributed to a cosmological asymmetry and to rules…
A reformulation of a physical theory in which measurements at the initial and final moments of time are treated independently is discussed, both on the classical and quantum levels. Methods of the standard quantum mechanics are used to…
The representation of a Schrodinger equations as a classic Hamiltonian system allows to construct a unified perturbation theory both in classic, and in a quantum mechanics grounded on the theory of canonical transformations, and also to…
The canonical description is presented for the string with pointlike masses at the ends in 1+1 dimensions in two different gauges: in the proper time gauge and in the light cone one. The classical canonical transformation is written out…
In this paper, we have firstly presented a new quantum theory to study one-dimensional photonic crystals. We give the quantum transform matrix, quantum dispersion relation and quantum transmissivity, and compare them with the classical…
It is explained how the unification of resonance and decay phenomena into a consistent mathematical theory leads to quantum mechanical time-asymmetry. This provides the theoretical basis for a subsequent paper II in which the interpretation…
We present a study on linear canonical transformation in the framework of a phase space representation of quantum mechanics that we have introduced in our previous work [1]. We begin with a brief recall about the so called phase space…
We characterize point transformations in quantum mechanics from the mathematical viewpoint. To conclude that the canonical variables given by each point transformation in quantum mechanics correctly describe the extended point…