Related papers: Few quantum mechanical models in higher dimension-…
General non-commutative supersymmetric quantum mechanics models in two and three dimensions are constructed and some two and three dimensional examples are explicitly studied. The structure of the theory studied suggest other possible…
We develop an approach for the treatment of one--dimensional bounded quantum--mechanical models by straightforward modification of a successful method for unbounded ones. We apply the new approach to a simple example and show that it…
Non-relativistic quantum mechanics is shown to emerge from classical mechanics through the requirement of a relativity principle based on special transformations acting on position and momentum uncertainties. These transformations keep the…
It is shown that quantum mechanics on noncommutative spaces (NQM) can be obtained by the canonical quantization of some underlying second class constrained system formulated in extended configuration space. It leads, in particular, to an…
Geometric (Schrodinger) quantization of nonrelativistic mechanics with respect to different reference frames is considered. In classical nonrelativistic mechanics, a reference frame is represented by a connection on a configuration space…
We generalize Maxwell equations which describe the vacuum of quantum electrodynamics into the quantum form. This nontraditional approach is different from the widely used theory|-Quantum Electrodynamics. From another viewpoint, it could be…
In the standard formulation of quantum mechanics, one starts by proposing a potential function that models the physical system. The potential is then inserted into the Schr\"odinger equation, which is solved for the wave function, bound…
The three-dimensional Schredinger's equation is analyzed with the help of the correspondence principle between classical and quantum-mechanical quantities. Separation is performed after reduction of the original equation to the form of the…
A discussion is given of the quantisation of a physical system with finite degrees of freedom subject to a Hamiltonian constraint by treating time as a constrained classical variable interacting with an unconstrained quantum state. This…
The non-Hermitian Schr\"odinger equation is re-expressed generally in the form of Hamilton's canonical equation without any approximation. Its quantization called non-Hermitian quantum field theory is discussed. By virtue of the canonical…
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…
General features of nonlinear quantum mechanics are discussed in the context of applications to two-level atoms.
New inverse and half-inverse problems: {\it sliding problems} are introduced. In this way several physically important equations are recovered from the quantum defect. In particular, sliding problems are solved for radial Schr\"odinger…
In an amended version of non-Hermitian interaction picture we propose to work with the states $\psi(t)$ in a dyadic representation. The control of evolution via two conjugate Schr\"{o}diner equations then renders the usual necessity of the…
Quantum computing has emerged as a promising avenue for achieving significant speedup, particularly in large-scale PDE simulations, compared to classical computing. One of the main quantum approaches involves utilizing Hamiltonian…
Third quantization is used in open quantum systems to construct a superoperator basis in which quadratic Lindbladians can be turned into a normal form. From it follows the spectral properties of the Lindbladian, including eigenvalues and…
A Fourier transformation in a fractional dimensional space of order $\la$ ($0<\la\leq 1$) is defined to solve the Schr\"odinger equation with Riesz fractional derivatives of order $\a$. This new method is applied for a particle in a…
We construct a variety of new exactly-solvable quantum systems, the potentials of which are given in terms of Lambert-W functions. In particular, we generate Schr\"odinger models with energy-dependent potentials, conventional Schr\"odinger…
The Lagrangian approach of Dirac is presented in a complete form. This suggests to identify the Schr\"{o}dinger equation as the Euler-Lagrange equation rather than the Hamiltonian operator equation.
The infinite dimensional generalization of the quantum mechanics of extended objects, namely, the quantum field theory of extended objects is employed to address the hitherto nonrenormalizable gravitational interaction following which the…