Related papers: Self-adjoint extensions and spectral analysis in C…
The goal of the present account is to review our efforts to obtain and apply a ``collective'' Hamiltonian for a few, approximately decoupled, adiabatic degrees of freedom, starting from a Hamiltonian system with more or many more degrees of…
In connection with the Fuglede conjecture, we study the existence of commuting self-adjoint extensions of the partial differential operators on arbitrary, possibly disconnected domains in $\br^d$, the associated unitary group, the spectral…
The quantum mechanical bound states of the $-{\alpha}/x^2$ potential are truly anomalous. We revisit this problem by adopting a slightly modified version of this potential, one that adopts a cutoff in the potential arbitrarily close to the…
This paper is devoted to the study of essential self-adjointness of a relativistic Schr\"{o}dinger operator with a singular homogeneous potential. From an explicit condition on the coefficient of the singular term, we provide a sufficient…
We study the momentum operator defined on the disjoint union of two intervals. Even in one dimension, the question of two non-empty open and non-overlapping intervals has not been worked out in a way that extends the cases of a single…
We investigate minimal operator corresponding to operator differential expression with exit from space, study its selfadjoint extensions, also for one particular selfadjoint extension corresponding to boundary value problem with some…
Due to its great importance for applications, we generalize and extend the approach of our previous papers to study aspects of the quantum and classical dynamics of a $4$-body system with equal masses in {\it $d$}-dimensional space with…
In these three lectures we will discuss some fundamental aspects of the theory of self-adjoint extensions of the covariant Laplace-Beltrami and Dirac operators on compact Riemannian manifolds with smooth boundary emphasizing the relation…
In the long wavelength limit, Maxwell-Chern-Simmon model and the dynamics of a particle in a plane under an external magnetic field perpendicular to that plane are identical. The self adjoint extension of such a problem depends on the value…
We solve the N-body Calogero problem, \ie N particles in 1 dimension subject to a two-body interaction of the form $\half \sum_{i,j}[ (x_i - x_j)^2 + g/ {(x_i - x_j)^2}]$, by constructing annihilation and creation operators of the form $…
Single particles moving in a reflection-asymmetric potential are investigated by solving the Schr\"{o}dinger equation of the reflection-asymmetric Nilsson Hamiltonian with the imaginary time method in 3D lattice space and the harmonic…
In 1964 J. M. Luttinger introduced a model for the quantum thermal transport. In this paper we study the spectral theory of the Hamiltonian operator associated to the Luttinger's model, with a special focus at the one-dimensional case. It…
In this thesis the quantum Hamilton - Jacobi (QHJ) formalism is used for (i) potentials which exhibit different spectra for different ranges of the potential parameters, (ii) exactly solvable (ES) periodic potentials (iii) quasi - exactly…
We compute the deficiency spaces of operators of the form $H_A{\hat{\otimes}} I + I{\hat{\otimes}} H_B$, for symmetric $H_A$ and self-adjoint $H_B$. This enables us to construct self-adjoint extensions (if they exist) by means of von…
The goal of this note is to present some arguments leading to the conjecture that a formally self-adjoint differential operator on a closed manifold is essentially self-adjoint if and only if the Hamiltonian flow of its symbol is complete.…
Scattering problem for a self-adjoint integro-differential operator, which is the sum of the operator of second derivative and of a finite-dimensional self-adjoint operator, is studied. Jost solutions are found and it is shown that the…
A similarity transformation is constructed through which a system of particles interacting with inverse-square two-body and harmonic potentials in one dimension, can be mapped identically, to a set of free harmonic oscillators. This…
Entanglement constitutes one of the key concepts in quantum mechanics and serves as an indispensable tool in the understanding of quantum many-body systems. In this work, we perform extensive numerical investigations of extensive…
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 study the isospectrality problem for a free quantum particle confined in a ring with a junction, analyzing all the self-adjoint realizations of the corresponding Hamiltonian in terms of a boundary condition at the junction. In…