Related papers: Strictly isospectral potentials from excited quant…
This work continues to study the set of quasi exactly solvable potentials related to the Eckart, Hult\'{e}n, Rosen-Morse, Coulomb and the harmonic oscillator potentials. We solve the Schr\"{o}dinger equation for each potential and obtain…
The presence of solvent tunes many properties of a molecule, such as its ground and excited state geometry, dipole moment, excitation energy, and absorption spectrum. Because the energy of the system will vary depending on the solvent…
We describe a new class of exact square integrable solutions of the Pauli and Dirac equation in rotating electromagnetic fields. Solutions obtained by putting equations in the stationary form with help of a coordinate transformation…
It is shown that the Dunkl harmonic oscillator on the line can be generalized to a quasi-exactly solvable one, which is an anharmonic oscillator with $n+1$ known eigenstates for any $n\in \N$. It is also proved that the Hamiltonian of the…
Under investigation in this work is the robust inverse scattering transform of the discrete Hirota equation with nonzero boundary conditions, which is applied to solve simultaneously arbitrary-order poles on the branch points and spectral…
The Darboux transformation operator technique in differential and integral forms is applied to the generalized Schrodinger equation with a position-dependent effective mass and with linearly energy-dependent potentials. Intertwining…
We show that the asymptotic formula for $\pi$, the Wallis formula, that was related with quantum mechanics and the hydrogen atom in \cite{HF}, can also be related to the harmonic oscillator using a quantum duality between these two systems.…
We optically probe the spectrum of ground and excited state transitions of an individual, electrically tunable self-assembled quantum dot molecule. Photocurrent absorption measurements show that the spatially direct neutral exciton…
In non-relativistic quantum mechanics, singular potentials in problems with spherical symmetry lead to a Schrodinger equation for stationary states with non-Fuchsian singularities both as r tends to zero and as r tends to infinity. In the…
Darboux-deformations of short range one-dimensional potentials are constructed by means of Gamow-Siegert functions (resonance states). Results include both Hermitian and non-Hermitian short range potentials which are exactly solvable. As…
We study fractional quantum Hall states in the cylinder geometry with open boundaries. By truncating the Coulomb interactions between electrons we show that it is possible to construct infinitely many exact eigenstates including the ground…
The interaction between two $\Xi$-type three-level atoms and a single-mode cavity field in the intensity dependent coupling regime has been studied. Exact analytical solution of the wave function for the considered atoms-field system has…
I revisit the problem of the interaction between two dissimilar atoms with one atom in an excited state, recently addressed by the authors of Refs.[1-3], and for which precedent approaches have given conflicting results. In the first place,…
Steady-state density functional theory, called i-DFT, is employed to compute spectral and transmission properties of general interacting nanoscale regions coupled to electronic reservoirs. Exchange-correlation functionals are constructed…
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…
For Klein-Gordon equation a consistent physical interpretation of wave functions is reviewed as based on a proper modification of the scalar product in Hilbert space. Bound states are then studied in a deep-square-well model where spectrum…
Exact analytical, closed-form solutions, expressed in terms of special functions, are presented for the case of a three-dimensional nonlinear quantum oscillator with a position dependent mass. This system is the generalization of the…
We study a simple model describing superradiance in a system of two-level atoms interacting with a single-mode bosonic field. The model permits a continuous crossover between integrable and partially chaotic regimes and shows a complex…
We compute, via a variational mixed-base method, the energy spectrum of a two dimensional relativistic atom in the presence of a constant magnetic field of arbitrary strength. The results are compared to those obtained in the…
We find broad classes of exact 4-dimensional asymptotically flat black hole solutions in Einstein-Maxwell theories with a non-minimally coupled dilaton and its non-trivial potential. We consider a few interesting limits, in particular, a…