Related papers: Exact solutions of effective-mass Schrodinger equa…
We show that the mass function method makes it much easier to obtain the exact solutions of Einstein equations. The known solutions for empty space and for the universe filled with dust-like matter are considered from the point of view of…
The physical condition that the expectation values of physical observables are real quantities is used to give a precise formulation of PT-symmetric quantum mechanics. A mathematically rigorous proof is given to establish the physical…
We obtain the exact energy spectrum of nonuniform mass particles for a collection of Hamiltonians in a three-dimensional approach to a quantum dot. By considering a set of generalized Schr\"odinger equations with different orderings between…
Simulations of supersymmetric field theories with spontaneously broken supersymmetry require in addition to the ultraviolet regularisation also an infrared one, due to the emergence of the massless Goldstino. The intricate interplay between…
A procedure to obtain the eigenenergies and eigenfunctions of a quantum spiked oscillator is presented. The originality of the method lies in an adequate use of asymptotic expansions of Wronskians of algebraic solutions of the Schroedinger…
We propose the notion of $E_{2}$-quasi-exact solvability and apply this idea to find explicit solutions to the eigenvalue problem for a non-Hermitian Hamiltonian system depending on two parameters. The model considered reduces to the…
We show that a recently proposed oscillator-shaped quantum well model associated with a position-dependent mass can be solved by applying a point canonical transformation to the constant-mass Schr\"odinger equation for the Scarf I…
We proposed a distributed approximating functional method for efficiently describing the electronic dynamics in atoms and molecules in the presence of the Coulomb singularities, using the kernel of a grid representation derived by using the…
The supersymmetric approach in the form of second order intertwining relations is used to prove the exact solvability of two-dimensional Schrodinger equation with generalized two-dimensional Morse potential for $a_0=-1/2$. This…
The concept of energy-dependent forces in quantum mechanics is re-analysed. We suggest a simplification of their study via the representation of each self-adjoint and energy-dependent Hamiltonian H=H(E) with real spectrum by an auxiliary…
The Schwarzschild solution is a complete solution of Einstein's field equations for a static spherically symmetric field. The Einstein's field equations solutions appear in the literature, but in different ways corresponding to different…
The electron states in axially symmetric quantum wires are computed by means of the effective-mass Schroedinger equation, which is written in cylindrical coordinates phi, rho, and z. We show that a direct discretization of the Schroedinger…
We construct two quantum spin chains Hamiltonians with quantum sl(2|1) invariance. These spin chains define variants of the Hubbard model and describe electron models with pair hoppings. A cubic algebra that admits the Birman-Wenzl-Murakami…
In this paper, we present efficient quantum algorithms that are exponentially faster than classical algorithms for solving the quantum optimal control problem. This problem involves finding the control variable that maximizes a physical…
It is shown that using the similarity transformations, a set of three-dimensional p-q nonlinear Schrodinger (NLS) equations with inhomogeneous coefficients can be reduced to one-dimensional stationary NLS equation with constant or varying…
Assuming that universe is the object of point rotation at a frequency, the relationship is established between this frequency and the cosmological constant. Using the transformation for point-like rotating coordinate systems, an unusual…
Using an isomorphism between Hilbert spaces $L^2$ and $\ell^{2}$ we consider Hamiltonians which have tridiagonal matrix representations (Jacobi matrices) in a discrete basis and an eigenvalue problem is reduced to solving a three term…
We present a class of solutions in Einstein-Yang-Mills-systems with arbitrary gauge groups and space-time dimensions, which are symmetric under the action of the group of spatial rotations. Our approach is based on the dimensional reduction…
We find a relationship between unitary transformations of the dynamics of quantum systems with time-dependent Hamiltonians and gauge theories. In particular, we show that the nonrelativistic dynamics of spin-$\frac12$ particles in a…
Using the pseudo-invariant operator method, we investigate the model of a particle with a time-dependent mass in a complex time-dependent symmetric potential well $V\left( x,t\right) =if\left(t\right) \left\vert x\right\vert$. The problem…