Related papers: E2-quasi-exact solvability for non-Hermitian model…
A method is suggested to obtain the quasi exact solution of the Rabi Hamiltonian. It is conceptually simple and can be easily extended to other systems. The analytical expressions are obtained for eigenstates and eigenvalues in terms of…
We present a self-consistent approach for computing the correlated quasiparticle spectrum of charged excitations in iterative $\mathcal{O}[N^5]$ computational time. This is based on the auxiliary second-order Green's function approach [O.…
We consider the non-Hermitian Hamiltonian H= -\frac{d^2}{dx^2}+P(x^2)-(ix)^{2n+1} on the real line, where P(x) is a polynomial of degree at most n \geq 1 with all nonnegative real coefficients (possibly P\equiv 0). It is proved that the…
We construct a variety of new exactly-solvable quantum systems, the potentials of which are given in terms of Lambert-W functions. In particular, we generate Schr\"odinger models with energy-dependent potentials, conventional Schr\"odinger…
We compare two recent approaches of quasi-exactly solvable Schr\" odinger equations, the first one being related to finite-dimensional representations of $sl(2,R)$ while the second one is based on supersymmetric developments. Our results…
We deform the real potential of Poeschl and Teller by a shift of its coordinate in imaginary direction. We show that the new model remains exactly solvable. Its bound states are constructed in closed form. Wave functions are complex and…
We present a theory of hypoellipticity and unique ergodicity for semilinear parabolic stochastic PDEs with "polynomial" nonlinearities and additive noise, considered as abstract evolution equations in some Hilbert space. It is shown that if…
The polynomial solution of the N-dimensional space Schrodinger equation for a special case of Mie potential is obtained for any arbitrary $% l-state. The exact bound-state energy eigenvalues and the corresponding eigenfunctions are…
Exactly-solvable Hamiltonians that can be diagonalized using relatively simple unitary transformations are of great use in quantum computing. They can be employed for decomposition of interacting Hamiltonians either in Trotter-Suzuki…
We present an approach for obtaining eigenfunctions of periodically driven time-dependent Hamiltonians. Assuming an approximate scale separation between two spatial regions where different potentials dominate, we derive an explicit…
Taking the Hydrogen atom as an example it is shown that if the symmetry of a three-dimensional system is $O(2) \oplus Z_2$, the variables $(r, \rho, \varphi)$ allow a separation of the variable $\varphi$, and the eigenfunctions define a new…
In this paper, we show that there is a large class of fermionic systems for which it is possible to find, for any dimension, a finite closed set of eigenoperators and eigenvalues of the Hamiltonian. Then, the hierarchy of the equations of…
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…
We develop a modified semi-classical approach to the approximate solution of Schrodinger's equation for certain nonlinear quantum oscillations problems. At lowest order, the Hamilton-Jacobi equation of the conventional semi-classical…
Schroedinger bound-state problem in D dimensions is considered for a set of central polynomial potentials (containing 2q coupling constants). Its polynomial (harmonic-oscillator-like, quasi-exact, terminating) bound-state solutions of…
In this paper we quantize the $N$-dimensional classical Hamiltonian system $H= \frac{|q|}{2(\eta + |q|)} p^2-\frac{k}{\eta +|q|}$, that can be regarded as a deformation of the Coulomb problem with coupling constant $k$, that it is smoothly…
It is shown that the $F_4$ rational and trigonometric integrable systems are exactly-solvable for {\it arbitrary} values of the coupling constants. Their spectra are found explicitly while eigenfunctions by pure algebraic means. For both…
We employ the point canonical transformation (PCT) to solve the D-dimensional Schr\"{o}dinger equation with position-dependent effective mass (PDEM) function for two molecular pseudoharmonic and modified Kratzer (Mie-type) potentials. In…
We present a new approach to compute selected eigenvalues and eigenvectors of the two-parameter eigenvalue problem. Our method requires computing generalized eigenvalue problems of the same size as the matrices of the initial two-parameter…
We use asymptotic analysis and numerical simulations to study peak-type singular solutions of the supercritical biharmonic NLS. These solutions have a quartic-root blowup rate, and collapse with a quasi self-similar universal profile, which…