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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.…
Time--dependent integrals of motion which are linear forms in position and momentum are discussed for Husimi parametric forced oscillator. Generalization of these integrals of motion for q--oscillator is presented. Squeezing and quadrature…
Let $S$ be a punctured Riemann surface with Euler characteristic $\chi(S)<0$. For any unitary representation $\rho: \pi_1(S) \to U(N)$, we introduce its renormalized energy and its harmonic representatives, which are equivariant harmonic…
By the method of generalized spherical harmonic polynomials, the Schr\"{o}dinger equation for a four-body system in $D$-dimensional space is reduced to the generalized radial equations where only six internal variables are involved. The…
We consider real symmetric and complex Hermitian random matrices with the additional symmetry $h_{xy}=h_{N-x,N-y}$. The matrix elements are independent (up to the fourfold symmetry) and not necessarily identically distributed. This ensemble…
We present a lattice model for polymer solutions, explicitly incorporating interactions with a bath of solvent and cosolvent molecules. By exploiting the well-known analogy between polymer systems and the $O(n)$-vector spin model in the…
We apply the asymptotic iteration method (AIM) to obtain the solutions of Schrodinger equation in the presence of Poschl-Teller (PT) potential. We also obtain the solutions of Dirac equation for the same potential under the condition of…
We introduce O-systems (Definition \ref{DO}) of orthogonal transformations of ${\Bbb R}^{m}$, and establish $1-1$ correspondences both between equivalence classes of Clifford systems and that of O-systems, and between O-systems and…
We extend to infinite dimensional separable Hilbert spaces the Schur convexity property of eigenvalues of a symmetric matrix with real entries. Our framework includes both the case of linear, selfadjoint, compact operators, and that of…
It has long been known that there exists a coordinate transformation which exactly maps the quantum free particle to the quantum harmonic oscillator. Here we extend this result by reformulating it as a unitary operation followed by a time…
We discuss the solutions of the Schroedinger equation for piecewise potentials, given by the harmonic oscillator potential for $\vert x\vert >a$ and an arbitrary function for $\vert x\vert <a$, using elementary methods. The study of this…
By factorization of the Hamiltonian describing the quantum mechanics of the continuous q-Hermite polynomial, the creation and annihilation operators of the q-oscillator are obtained. They satisfy a q-oscillator algebra as a consequence of…
We present an O(N) algorithm to study the vibrational properties of amorphous silicon within the framework of tight-binding approach. The dynamical matrix elements have been evaluated numerically in the harmonic approximation exploiting the…
New examples of matrix quasi exactly solvable Schroedinger operators are constructed. One of them constitutes a matrix generalization of the quasi exactly solvable anharmonic oscillator, the corresponding invariant vector space is…
The study of SU(N) quantum spin models is relevant to a variety of physical systems including ultracold atoms in optical lattices, and also leads to insights into novel quantum phases and phase transitions of SU(2) spin models. We use…
In the present work, we studied the q-deformed Morse and harmonic oscillator systems with appropriate canonical commutation algebra. The analytic solutions for eigenfunctions and energy eigenvalues are worked out using time-independent…
We consider quantum systems which interact strongly with a rapidly varying environment and derive a Schrodinger-like equation which describes the time evolution of the average wave function. We show that the corresponding Hamiltonian can be…
A "microscopic" justification of the "symmetric damping" model of a quantum oscillator with time-dependent frequency and time-dependent damping is given. This model is used to predict results of experiments on simulating the dynamical…
We perform an extensive bootstrap study of Hermitian and non-Hermitian theories based on the novel analytic continuation of $\langle\phi^n\rangle$ or $\langle(i\phi)^n\rangle$ in $n$. We first use the quantum harmonic oscillator to…
In a recent paper by Jafarov, Nagiyev, Oste and Van der Jeugt (2020 {\sl J.\ Phys.\ A} {\bf 53} 485301), a confined model of the non-relativistic quantum harmonic oscillator, where the effective mass and the angular frequency are dependent…