Related papers: Conditionally exactly solvable potential and dual …
The complete integrability of a class of dynamical systems with the potential v(q)=q^{-2}+c q^2 is proved.
Using supersymmetric quantum mechanics we construct the quasi-exactly solvable (QES) potentials with arbitrary two known eigenstates. The QES potential and the wave functions of the two energy levels are expressed by some generating…
We present a simple proof of quantum contextuality for a spinless particle with a one dimensional configuration space. We then discuss how the maximally realistic deterministic quantum mechanics recently constructed by this author and V.…
We present a general procedure for determining quasi-exact solvability of the Dirac and the Pauli equation with an underlying $sl(2)$ symmetry. This procedure makes full use of the close connection between quasi-exactly solvable systems and…
The procedure proposed recently by J.Bougie, A.Gangopadhyaya and J.V.Mallow to study the general form of shape invariant potentials in one-dimensional Supersymmetric Quantum Mechanics (SUSY QM) is generalized to the case of Higher Order…
New exactly solvable quantum models are obtained with the help of the supersymmetric extencion of the nonstationary Schr/"odinger equation.
New types of irreducible second order Darboux transformations for the one dimensional Schroedinger equation are described. The main feature of such transformations is that the transformation functions have the eigenvalues grater then the…
We study a class of Calogero-Sutherland type one dimensional N-body quantum mechanical systems, with potentials given by $$ V( x_1, x_2, \cdots x_N) = \sum_{i <j} {g \over {(x_i - x_j)^2}} - \frac{g^{\prime}}{\sum_{i<j}(x_i - x_j)^2} +…
In this paper, we present in detail consistent QED (and scalar QED) calculations of particle creation effects in external electromagnetic field that correspond to three most important exactly solvable cases of t-electric potential steps:…
The one-dimensional Coulomb-like potential with a real coupling constant beta, and a centrifugal-like core of strength G = alpha^2 - {1/4}, viz. V(x) = {alpha^2 - (1/4)}/{(x-ic)^2} + beta/|x-ic|, is discussed in the framework of…
We consider a superintegrable Hamiltonian system in a two-dimensional space with a scalar potential that allows one quadratic and one cubic integral of motion. We construct the most general cubic algebra and we present specific…
Dualities and duality transformations form a well established methodology in various aspects of quantum many body physics and quantum field theories, allowing one to exploit equivalence between models which may naively seem completely…
Examples are given of q-deformed systems that may be interpreted by the standard rules of quantum theory in terms of new degrees of freedom and supplementary quantum numbers.
A general algebraic procedure for constructing coherent states of a wide class of exactly solvable potentials e.g., Morse and P{\"o}schl-Teller, is given. The method, {\it a priori}, is potential independent and connects with earlier…
Supersymmetric Quantum Mechanics may be used to construct reflectionless potentials and phase-equivalent potentials. The exactly solvable case of the $\lambda sech^2$ potential is used to show that for certain values of the strength…
Various quasi-exact solvability conditions, involving the parameters of the periodic associated Lam{\'e} potential, are shown to emerge naturally in the quantum Hamilton-Jacobi approach. It is found that, the intrinsic nonlinearity of the…
The conventional Hamiltonian $H= p^2+ V_N(x)$, where the potential $V_N(x)$ is a polynomial of degree $N$, has been studied intensively since the birth of quantum mechanics. In some cases, its spectrum can be determined by combining the WKB…
There exists an exact relationship between the quasi-exactly solvable problems of quantum mechanics and models of square and rectangular random complex matrices. This relationship enables one to reduce the problem of constructing…
In supersymmetric quantum mechanics, exact-solvability of one-dimensional quantum systems can be classified only with an additional assumption of integrability, the so-called shape invariance condition. In this paper we show that in the…
We construct exactly solvable models for four particles moving on a real line or on a circle with translation invariant two- and four-particle interactions.