Related papers: On the misinterpretation of conditionally-solvable…
We study the existence of formal power series solutions to q-algebraic equations. When a solution exists, we give a sufficient condition on the equation for this solution to have a positive radius of convergence. We emphasize on the case…
We present a formulation of quantum mechanics based on orthogonal polynomials. The wavefunction is expanded over a complete set of square integrable basis in configuration space where the expansion coefficients are orthogonal polynomials in…
A comprehensive review of exactly solvable quantum mechanics is presented with the emphasis of the recently discovered multi-indexed orthogonal polynomials. The main subjects to be discussed are the factorised Hamiltonians, the general…
We derive some properties of the hydrogen atom inside a box with an impenetrable wall that have not been discussed before. Suitable scaling of the Hamiltonian operator proves to be useful for the derivation of some general properties of the…
Some recent experiments claim to show that any model in which a quantum state represents mere information about an underlying physical reality of the system must make predictions which contradict those of quantum theory. The present work…
We generalize a recently proposed small-energy expansion for one-dimensional quantum-mechanical models. The original approach was devised to treat symmetric potentials and here we show how to extend it to non-symmetric ones. Present…
In this paper we provide a general account of the causal models which attempt to provide a solution to the famous measurement problem of Quantum Mechanics (QM). We will argue that --leaving aside instrumentalism which restricts the physical…
Within the frame of a novel treatment we make a complete mathematical analysis of exactly solvable one-dimensional quantum systems with non-constant mass, involving their ordering ambiguities. This work extends the results recently reported…
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…
The main difficulty of quantum field theory is the problem of divergences and renormalization. However, realistic models of quantum field theory are renormalized within the perturbative framework only. It is important to investigate…
An experimental study of the applicability of mechanics equations to describing the process of equilibrium establishing in an isolated spin system was performed. The time-reversion effects were used at the experiments. It was demonstrated,…
The quantum mechanical equivalent of parametric resonance is studied. A simple model of a periodically kicked harmonic oscillator is introduced which can be solved exactly. Classically stable and unstable regions in parameter space are…
Geometrical model for quantum objects is suggested. It is shown that equations for free material Dirac field and for Maxwell electromagnetic field can be considered as relations describing propagation of the space topological defects. This…
The paper reviews and discusses four ideas scattered in previous papers of the author. First, objective properties of quantum systems are not associated with observables but are defined by preparations. Second, measurable results of…
The linear mathematics of quantum mechanics gives many versions of reality instead of the single version we perceive, with the perceived version chosen at random according to a probability law. Because of these peculiarities, the theory…
In this paper, we investigate a class of nonlinear eigenvalue problems resulting from quantum physics. We first prove that the eigenfunction cannot be a polynomial on any open set, which may be reviewed as a refinement of the classic unique…
We give a brief overview of a simple and unified way, called the prepotential approach, to treat both exact and quasi-exact solvabilities of the one-dimensional Schr\"odinger equation. It is based on the prepotential together with Bethe…
We will provide detailed arguments showing that the set of Maxwell equations, and the corresponding wave equations, do not properly describe the evolution of electromagnetic wave-fronts. We propose a nonlinear corrected version that is…
A transformation method is applied to the second order ordinary differential equation satisfied by orthogonal polynomials to construct a family of exactly solvable quantum systems in any arbitrary dimensional space. Using the properties of…
A few quasi-exactly solvable models are studied within the quantum Hamilton-Jacobi formalism. By assuming a simple singularity structure of the quantum momentum function, we show that the exact quantization condition leads to the condition…