Krylov complexity measures operator growth with respect to a basis, which is adapted to the
Heisenberg time evolution. The construction of that basis relies on the Lanczos algorithm …

Transfer of data in linear quantum registers can be significantly simplified with
preengineered but not dynamically controlled interqubit couplings. We show how to …

Relativistic effects are of major importance for understanding the properties of heavier atoms
and molecules. Volumes I-III of Relativistic Theory of Atoms and Molecules constitute the …

We extended exactly solvable model of a nonrelativistic quantum linear harmonic oscillator
with a position-dependent mass\(M\left (x\right)=\frac {{a}^{2}{m} _ {0}}{{a}^{2}+{x}^{2}}\) to …

Finite oscillator models obey the same dynamics as the classical and quantum oscillators,
but the operators corresponding to position, momentum, Hamiltonian, and angular …

The Jaynes-Cummings-Hubbard (JCH) system describes a network of single-mode photonic
cavities connected via evanescent coupling. Each cavity contains a single two-level system …

We obtain the time-dependent correlation function describing the evolution of a single spin
excitation state in a linear spin chain with isotropic nearest-neighbour XY coupling, where …

Starting from the Rodrigues formula we present a general construction of raising and
lowering operators for orthogonal polynomials of continuous and discrete variables on a …

A finite two-dimensional radial oscillator of (N+ 1) 2 points is proposed, with the dynamical
Lie algebra so (4)= su (2) x⊕ su (2) y examined in part I of this work, but reduced by a …

The Kravchuk and Meixner polynomials of discrete variable are introduced for the discrete
models of the harmonic oscillator and hydrogen atom. Starting from Rodrigues formula we …