Related papers: Position-dependent mass systems: Classical and qua…

We apply the supersymmetry approach to one-dimensional quantum systems with spatially-dependent mass, by including their ordering ambiguities dependence. In this way we extend the results recently reported in the literature. Furthermore, we…

This paper collects and extends the lectures I gave at the "XXIV International Fall Workshop on Geometry and Physics" held in Zaragoza (Spain) August 31 - September 4, 2015. Within these lectures I review the formulation of Quantum…

This is an extended version of the talk given by the Author at the 40th Symposium on Mathematical Physics held in Torun, Poland, June 25-28, 2008. We review the methods of canonical quantization of free particle motion on curved…

We present the quantum and classical mechanics formalisms for a particle with position-dependent mass in the context of a deformed algebraic structure (named $\kappa$-algebra), motivated by the Kappa-statistics. From this structure we…

This is the abstract of a series of lectures given during the XIIIth School on Geometry and Physics, Bialystok (Poland), in July 2024. In this minicourse, we first examine the algebraic aspects of barycentric algebras. Then, we focus on…

An inhomogeneous Kaluza-Klein compactification to four dimensions, followed by a conformal transformation, results in a system with position dependent mass (PDM). This origin of a PDM is quite different from the condensed matter one. A…

3d quantum mechanical systems with position dependent masses (PDM) admitting at least one second order integral of motion and symmetries with respect to dilatation or shift transformations are classified. Twenty-seven such systems are…

These notes partly touch the topic of the talk given by the author at the XXXVIII Workshop on Geometric Methods in Physics, hold in June-July 2019 in Bia\l{}owie\.{z}a, Poland. They consist of a short and self-contained introduction to the…

This text contains lecture notes of the course taught to Ph.D. students of Jagiellonian University in Krakow on 25-28 November, 2013.

These notes are based on a lecture given by S. L. Woronowicz at the Institute of Mathematics, Polish Academy of Sciences.

A generalized scheme for the construction of coherent states in the context of position-dependent effective mass systems has been presented. This formalism is based on the ladder operators and associated algebra of the system which are…

In these four lectures I describe basic ideas and methods applicable to both classical and quantum systems displaying slow relaxation and non-equilibrium dynamics. The first half of these notes considers classical systems, and the second…

Using concepts of geometric orthogonality and linear independence, we logically deduce the form of the Pauli spin matrices and the relationships between the three spatially orthogonal basis sets of the spin-1/2 system. Rather than a…

Position holds a very special role in understanding the classical behaviour of macroscopic bodies on the basis of quantum principles. This lead us to examine the localised states of a large condensed object in the context of a realistic…

In this paper, we use methods from differential geometry and statistical mechanics to investigate a model for the concept of mass. The theory is not quantum mechanical in the usual sense, although certain features like multiple histories…

We analyse a relativistic scalar particle with a position-dependent mass in a spacetime with a space-like dislocation by showing that relativistic bound states solutions can be achieved. Further, we consider the presence of the Coulomb…

To enhance the consistency between the quantum descriptions of waves and particles, we quantise mechanical point particles in this paper in the same physically-motivated way as we previously quantised light in quantum electrodynamics…

The motion of astronomical bodies and the centre of mass of the system is not always well perceived by students. One of the struggles is the conceptual change of reference frame, which is the same that held back the acceptance of the…

This article is based on the opening lecture at the third quantum geometry and quantum gravity school sponsored by the European Science Foundation and held at Zakopane, Poland in March 2011. The goal of the lecture was to present a broad…

Superintegrable Hamiltonian systems describing the interactions among three point masses on a line have been described in [2]. Here, we show examples of how the approach of above can be extended to a higher number of particles on a line and…