Related papers: Quantum mechanics with coordinate-dependent mass
In this work, we develop a mathematical framework to model a quantum system whose Hamiltonian may depend on the state of changing environment, that evolves according to a Markovian process. When the environment changes its state, the…
We study the commutation relations, uncertainty relations and spectra of position and momentum operators within the framework of quantum group % symmetric Heisenberg algebras and their (Bargmann-) Fock representations. As an effect of the…
We study the Hamiltonian equations of motion of a heavy tracer particle interacting with a dense weakly interacting Bose-Einstein condensate in the classical (mean-field) limit. Solutions describing ballistic subsonic motion of the particle…
The main goal of these lectures -- introduction to Quantum Mechanics for mathematically-minded readers. The second goal is to discuss the mathematical interpretation of the main quantum postulates: transitions between quantum stationary…
We study evolution of a quantum particle in a harmonic potential whose position and momentum are repeatedly monitored. A back-action of measuring devices is accounted for. Our model utilizes a generalized measurement corresponding to the…
We study the classical and quantum oscillator in the context of a non-additive (deformed) displacement operator, associated with a position-dependent effective mass, by means of the supersymmetric formalism. From the supersymmetric partner…
Position and momentum observables are considered and their correlation is studied for the simplest quantum system of a free particle moving in one dimension. The algebra and the eigenvalue problem for the correlation observable is presented…
A foundation of quantum mechanics based on the concepts of focusing and symmetry is proposed. Focusing is connected to c-variables - inaccessible conceptually derived variables; several examples of such variables are given. The focus is…
In this paper we review a proposed geometrical formulation of quantum mechanics. We argue that this geometrization makes available mathematical methods from classical mechanics to the quantum frame work. We apply this formulation to the…
This paper analyses quantum mechanics in multiply connected spaces. It is shown that the multiple connectedness of the configuration space of a physical system can determine the quantum nature of physical observables, such as the angular…
The Hermiticity condition in quantum mechanics required for the characterisation of (a) physical observables and (b) generators of unitary motions can be relaxed into a wider class of operators whose eigenvalues are real and whose…
We develop a quantum model based on the correspondence between energy distribution between harmonic oscillators and the partition of an integer number. A proper choice of the interaction Hamiltonian acting within this manifold of states…
A translation operator is introduced to describe the quantum dynamics of a position-dependent mass particle in a null or constant potential. From this operator, we obtain a generalized form of the momentum operator as well as a unique…
We explore the emergence of many-body physics from quantum mechanics via spontaneous symmetry breaking. To this end, we study potentials which are functionals on the space of Hamiltonians enjoying an unstable critical point corresponding to…
We investigate the transition from quantum to classical mechanics using a one-dimensional free particle model. In the classical analysis, we consider the initial positions and velocities of the particle drawn from Gaussian distributions.…
The momentum representation is seldom used in quantum mechanics courses. Some students are thence surprised by the change in viewpoint when, in doing advanced work, they have to use the momentum rather than the coordinate representation. In…
We consider electrodynamics on a noncommutative spacetime using the enveloping algebra approach and perform a non-relativistic expansion of the effective action. We obtain the Hamiltonian for quantum mechanics formulated on a canonical…
A formulation of quantum mechanics, which begins by postulating assertions for individual physical systems, is given. The statistical predictions of quantum mechanics for infinite ensembles are then derived from its assertions for…
Low-energy transport in quantum Hall states is carried through edge modes, and is dictated by bulk topological invariants and possibly microscopic Boltzmann kinetics at the edge. Here we show how the presence or breaking of symmetries of…
Bohmian mechanics is a theory about point particles moving along trajectories. It has the property that in a world governed by Bohmian mechanics, observers see the same statistics for experimental results as predicted by quantum mechanics.…