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The coupled motion is investigated for a mechanical system consisting of water and a body freely floating in it. Water occupies either a half-space or a layer of constant depth into which an infinitely long surface-piercing cylinder is…
The known approaches of number-phase problem (for a quantum oscillator) are mutually contradictory. All of them are subsequent in respect with the Robertson-Schr\"{o}dinger uncertainty relation (RSUR). In oposition here it is proposed a new…
We examine random matrix systems driven by an external field in view of optimal control theory (OCT). By numerically solving OCT equations, we can show that there exists a smooth transition between two states called "moving bases" which are…
In some previous works, two of the authors have introduced a strategy to develop high-order numerical methods for systems of balance laws that preserve all the stationary solutions of the system. The key ingredient of these methods is a…
The overview of the Exact Pairing technique based on the quasispin symmetry is presented. Extensions of this method are discussed in relation to mean field, quadrupole collectivity, electromagnetic transitions, and many-body level density.…
Using the basic ingredient of supersymmetry, we develop a simple alternative approach to perturbation theory in one-dimensional non-relativistic quantum mechanics. The formulae for the energy shifts and wave functions do not involve tedious…
We present a method for incorporating a stochastic point of view into physics exercises of mathematics education. The core of our method is the randomization of some inputs, the system model used does not differ from what we would use in…
Many exactly solvable models are based on Lie algebras. The pairing interaction is important in nuclear physics and its exact solution for identical particles in non-degenerate single-particle levels was first given by Richardson in 1963.…
The use of dynamical symmetries or spectrum generating algebras for the solution of the nuclear many-body problem is reviewed. General notions of symmetry and dynamical symmetry in quantum mechanics are introduced and illustrated with…
We examine mathematical questions around angle (or phase) operator associated with a number operator through a short list of basic requirements. We implement three methods of construction of quantum angle. The first one is based on operator…
A general introduction is given to what can be predicated about quantum gravity once the lessons from the standard model of particle physics are taken into account. In particular, the effective lagrangian point of view is briefly commented…
Control-based continuation (CBC) is an experimental method that can reveal stable and unstable dynamics of physical systems. It extends the path-following principles of numerical continuation to experiments, and provides systematic…
The Dirac oscillators are shown to be an excellent expansion basis for solutions of the Dirac equation by $R$-matrix techniques. The combination of the Dirac oscillator and the $R$-matrix approach provides a convenient formalism for…
We present a novel scheme for nuclear structure calculations based on realistic nucleon-nucleon potentials. The essential ingredient is the explicit treatment of the dominant interaction-induced correlations by means of the Unitary…
We present an algebraic approach to the internal structure of baryons in terms of three constituents. We investigate a collective model in which the nucleon is regarded as a rotating and vibrating oblate top with a prescribed distribution…
A common problem in physics and engineering is determination of the orientation of an object given its angular velocity. When the direction of the angular velocity changes in time, this is a nontrivial problem involving coupled differential…
The unitary gauge fixing technique is applied to the QCD hamiltonian formulated in terms of angular variables. It is demonstrated that in this formulation projections on the physical Hilbert space are unnecessary to separate physical and…
A review of methods for finding general expressions for matrix elements (non-diagonal with respect to configurations included) of any one- and two-particle operator for an arbitrary number of shells in an atomic configuration is given.…
We draw attention to some tune problems in constructions of the quantum-field operators for spins 1/2 and 1. They are related to the existence of negative-energy and acausal solutions of relativistic wave equations. Particular attention is…
Robust control of quantum systems is an increasingly relevant field of study amidst the second quantum revolution, but there remains a gap between taming quantum physics and robust control in its modern analytical form that culminated in…