Related papers: New Approach to Bounded Quantum--Mechanical Models
A unified approach, for solving a wide class of single and many-body quantum problems, commonly encountered in literature is developed based on a recently proposed method for finding solutions of linear differential equations. Apart from…
We present a scheme for controlling the state of a quantum system by modifying the boundary conditions. This constitutes an infinite-dimensional control problem. We provide conditions for the existence of solutions of the dynamics and prove…
A reformulation of a physical theory in which measurements at the initial and final moments of time are treated independently is discussed, both on the classical and quantum levels. Methods of the standard quantum mechanics are used to…
An application of a quantum wave impedance method for a study of quantum-mechanical systems which con\-tain singular zero-range potentials is considered. It was shown how to reformulate the problem of an investigation of mentioned systems…
We discuss a systematic construction of dimensionless quantum-mechanical equations. The process reduces the number of independent model parameters to a minimum and, at the same time, provides the natural units of length, energy, etc. in a…
This thesis is focused on some solvable quantum mechanical models and their associated symmetries.
A new parameter-free method is proposed for treatment of single-particle resonances in the real-energy continuum shell model. This method yields quasi-bound states embedded in the continuum which provide a natural generalization of weakly…
We propose two improvements to the well-known power series method for confined one-dimensional quantum-mechanical problems. They consist of the addition of a variational step were the energy plays the role of a variational parameter. We…
A longstanding problem in quantum metrology is how to extract as much information as possible in realistic scenarios with not only multiple unknown parameters, but also limited measurement data and some degree of prior information. Here we…
The paper is an attempt to generalize a methodology, which is similar to the bounded-input bounded-output method currently widely used for the system stability studies. The presented earlier methodology allows decomposition of input space…
Quantum mechanics/molecular mechanics (QM/MM) hybrid models allow one to address chemical phenomena in complex molecular environments. Whereas this modeling approach can cope with a large system size at moderate computational costs, the…
We introduce a particular nonlinear generalization of quantum mechanics which has the property that it is exactly solvable in terms of the eigenvalues and eigenfunctions of the Hamiltonian of the usual linear quantum mechanics problem. We…
Modelling quantum devices is to find a model according to quantum theory that can explain the result of experiments in a quantum device. We find that usually we cannot correctly identify the model describing the actual physics of the device…
A new framework for deriving equations of motion for constrained quantum systems is introduced, and a procedure for its implementation is outlined. In special cases the framework reduces to a quantum analogue of the Dirac theory of…
We present a unified approach for solving and classifying exactly solvable potentials. Our unified approach encompasses many well-known exactly solvable potentials. Moreover, the new approach can be used to search systematically for a new…
Quantum computing promises to speed up some of the most challenging problems in science and engineering. Quantum algorithms have been proposed showing theoretical advantages in applications ranging from chemistry to logistics optimization.…
We analyze constrained quantum systems where the dynamics do not preserve the constraints. This is done in particular for the restriction of a quantum particle in Euclidean n-space to a curved submanifold, and we propose a method of…
We describe a method of solving quantum field theories using operator techniques based on the expansion of interacting fields in terms of asymptotic fields. For bound states, we introduce an asymptotic field for each (stable) bound state.…
One-to-one reversible automata are introduced. Their applicability to a modelling of the quantum mechanical measurement process is discussed.
New status in quantum mechanics is connected with recent achievements in the inverse problem. With its help instead of about ten exactly solvable models which serve as a basis of the contemporary education there are infinite (!) number,…