Related papers: Operator based approach to PT-symmetric problems o…
We show that quantum Bateman's system which arises in the quantization of a damped harmonic oscillator is equivalent to a quantum problem with 2D parabolic potential barrier known also as 2D inverted isotropic oscillator. It turns out that…
An approach to study a generalization of the classical-quantum transition for general systems is proposed. In order to develop the idea, a deformation of the ladder operators algebra is proposed that contains a realization of the quantum…
Parity-time (PT) symmetric systems have two distinguished phases, e.g., one with real energy eigenvalues and the other with complex conjugate eigenvalues. To enter one phase from the other, it is believed that the system must pass through…
We introduce a new operator algebra for the description of the low-energy physics of one-dimensional, integrable, multicomponent quantum liquids. Considering the particular case of the Hubbard chain in a constant external magnetic field and…
We consider a symmetric block operator spectral problem with two spectral parameters. Under some reasonable restrictions, we state localisation theorems for the pair-eigenvalues and discuss relations to a class of non-self-adjoint spectral…
A path-integral approach for the computation of quantum-mechanical propagators and energy Green's functions is presented. Its effectiveness is demonstrated through its application to singular interactions, with particular emphasis on the…
This is a survey of recent results on zeta- and eta-function poles and values for realizations of Laplace- and Dirac-type operators defined by pseudodifferential projection boundary conditions (including the Atiyah-Patodi-Singer operator…
Given a self-adjoint operator $T$ on a separable infinite-dimensional Hilbert space we study the problem of characterizing the set $\mathcal D(T)$ of all possible diagonals of $T$. For operators $T$ with at least two points in their…
In 1998, Carl Bender challenged the perceived wisdom of quantum mechanics that the Hamiltonian operator describing any quantum mechanical system has to be Hermitian. He showed that Hamiltonians that are invariant under combined parity-time…
In this article we have investigated some of the theoretical aspects of the solutions of quantum mechanical equations in Rindler space. We have developed the formalism for exact analytical solutions for Schr$\ddot{\rm{o}}$dinger equation…
Extending the supersymmetric method proposed by Tkachuk to the complex domain, we obtain general expressions for superpotentials allowing generation of quasi-exactly solvable PT-symmetric potentials with two known real eigenvalues (the…
In this paper, we use a probabilistic approach to show that there exists a unique, bounded continuous solution to the Dirichlet boundary value problem for a general class of second order non-symmetric elliptic operators $L$ with singular…
We determine a fundamental solution for the differential operator (Delta - lambda_z)^n on the Riemannian symmetric space G/K, where G is any complex semi-simple Lie group, and K is a maximal compact subgroup. We develop a global zonal…
We construct PT-symmetric quantum mechanical models with an O(N)-symmetric interaction term of the form $-g(\vec{x}^{2})^{2}/N$. Using functional integral methods, we find the equivalent Hermitian model, which has several unusual features.…
We consider two-point non-self-adjoint boundary eigenvalue problems for linear matrix differential operators. The coefficient matrices in the differential expressions and the matrix boundary conditions are assumed to depend analytically on…
The algebraic approach to operator perturbation method has been applied to two quantum--mechanical systems ``The Stark Effect in the Harmonic Oscillator'' and ``The Generalized Zeeman Effect''. To that end, two realizations of the…
Recent advances in the theory of complex symmetric operators are presented and related to current studies in non-hermitian quantum mechanics. The main themes of the survey are: the structure of complex symmetric operators, $C$-selfadjoint…
Adapting the method of Andrews-Clutterbuck we prove an eigenvalue gap theorem for a class of non symmetric second order linear elliptic operators on a convex domain in euclidean space. The class of operators includes the Bakry-Emery…
We consider classical N-particle system with arbitrary central pair potential. Mechanical equilibrium condition in spherically-symmetric case leads to a nonlinear integro-differential equation for concentration n(r). For special state…
In this note, we study the potential algebra for several models arising out of quantum mechanics with generalized uncertainty principle. We first show that the eigenvalue equation corresponding to the momentum-space Hamiltonian…