Related papers: Simple quantum systems in the momentum representat…
Quantum systems are dynamic systems restricted by the principles of quantum mechanics (linearity of dynamic equations, linear transformation of the wave function etc.). One suggests to investigate the quantum systems simply as dynamic…
We show in this paper that the basic representations of position and momentum in a quantum mechanical system, that are guided by a generalized uncertainty principle and lead to a corresponding one-parameter eigenvalue problem, can be…
The formulation of quantum mechanics on spaces of constant curvature is studied. It is shown how a transition from a classical system to the quantum case can be accomplished by the quantization of the Noether momenta. These can be…
We introduce new representations to formulate quantum mechanics on noncommutative phase space, in which both coordinate-coordinate and momentum-momentum are noncommutative. These representations explicitly display entanglement properties…
Classical transport equations with probabilistic initial conditions can be viewed as quantum systems. In a discrete version they are probabilistic automata. The time-local probabilistic information is encoded in a classical wave function.…
In this paper a didactic approach is described which immediately leads to an understanding of those postulates of quantum mechanics used most frequently in quantum computation. Moreover, an interpretation of quantum mechanics is presented…
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…
A new derivation is given of the known generalized position-momentum uncertainty relation, which takes into account gravity. The problem of two massive particles, the relative motion of which is described by the Schroedinger equation, is…
The supposed equivalence of the conventional interpretation of quantum mechanics with Bohm's interpretation is generally demonstrated only in the coordinate representation. It is shown, however, that in the momentum representation this…
It is shown that general solutions of the free-particle Schroedinger equation can be mapped onto solutions of the Schroedinger equation for the harmonic oscillator. This is done in such a way that the time evolution of a free particle…
A physical theory is proposed that obeys both the principles of special relativity and of quantum mechanics. As a key feature, the laws are formulated in terms of quantum events rather than of particle states. Temporal and spatial…
The convenience of coherent state representation is discussed from the viewpoint of what is in a broad sense called the measurement problem in quantum mechanics. Standard quantum theory in coherent state representation is intrinsically…
The hierarchy of equations for reduced density matrices that describes a thermodynamically equilibrium quantum system obtained earlier by the author is investigated in the momentum representation. In the paper it is shown that the use of…
We consider the quantum mechanics of a particle on a noncommutative plane. The case of a charged particle in a magnetic field (the Landau problem) with a harmonic oscillator potential is solved. There is a critical point, where the density…
Integrable quantum mechanical systems for neutral particles with spin $\frac12$ and nontrivial dipole momentum are classified. It is demonstrated that such systems give rise to new exactly solvable problems of quantum mechanics with clear…
In this paper, we demonstrate novel relationships between quantum mechanics and the electromagnetic wave equation. In our approach, an invariant interference-dependent electromagnetic quantity, which we call "quantum rest mass", replaces…
The fundamental principle of quantum mechanics is that the probabilities of physical outcomes are obtained from the intermediate states and processes of the interacting particles, considered as happening concurrently. When the interaction…
A contradiction arises when applying standard boundary conditions to a simple quantum rotator with a single coordinate. New boundary conditions for the Schroedinger equation are proposed that involve only gauge invariant quantities, and…
Students in a quantum mechanics course are often introduced to the Schr\"odinger equation as the standard mathematical tool. However, rarely do students develop an understanding as to why the equation is the choice for modeling quantum…
A new discrete model for energy relaxation of a quantum particle is described via a projection operator, causing the wave function collapse. Power laws for the evolution of the particle coordinate and momentum dispersions are derived. A new…