Related papers: T-matrix in discrete oscillator representation
We study two classes of radial integrals involving a product of bound and continuum one-electron states. Using a representation of the continuum part with an expansion on complex Gaussian Type Orbitals, such integrals can be performed…
Resonance phenomena are central to many quantum systems, where resonant states are typically characterized by pole singularities of the S-matrix. In this work, we employ the complex scaling method (CSM) in conjunction with exact WKB…
We consider Green's functions $G(z):=(H-z)^{-1}$ of Hermitian random band matrices $H$ on the $d$-dimensional lattice $(\mathbb Z/L\mathbb Z)^d$. The entries $h_{xy}=\bar h_{yx}$ of $H$ are independent centered complex Gaussian random…
We exactly calculate the momentum-dependent critical exponents for spectral functions in the one-dimensional anisotropic t-J models with a gap either in the spin or charge excitation spectrum. Our approach is based on the Bethe ansatz…
The object of this laboratory work: to explore dependence mass point oscillatory motion parameters in the following cases: - without resistance (free oscillations); - the resistance force is proportional to the velocity vector; - the…
The aim of this paper is to study differential and spectral properties of the infinitesimal operator of two dimensional Markov processes with diffusion and discrete components. The infinitesimal operator is now a second-order differential…
We present a new algorithm for computing the Lyapunov exponents spectrum based on a matrix differential equation. The approach belongs to the so called continuous type, where the rate of expansion of perturbations is obtained for all times,…
We introduce two-parameter classes of exactly-solvable novel systems whose Hamiltonian operators could be represented by tridiagonal symmetric matrices in some orthogonal bases. The associated wavefunction is written as point-wise…
Matrix mechanics is an important component of an undergraduate education in quantum mechanics. In this paper we present several examples of the use of matrix mechanics to solve for a number of three dimensional problems involving central…
A nonpolynomial one-dimensional quantum potential in the form of an isotonic oscillator (harmonic oscillator with a centripetal barrier) is studied. We provide the non-relativistic bound state energy spectrum E_{n} and the wave functions…
We analyze the possible expansions of the interatomic potential $U(|\textbf{r}_{1}-\textbf{r}_{2}|)$ in a Fourier series for a cyclic system and a system with boundaries. We also study the transition from exact expansions for a finite…
The quantum propagator and characteristic equation in the presence of a chain of $\delta$-potentials are obtained in the rectangular, cylindrical and spherical coordinate systems. The simplicity and efficiency of the method is illustrated…
We derive a generalized Low equation for the T-matrix appropriate for complex atom-molecule interaction. The properties of this new equation at very low energies are studied and the complex scattering length and effective range are derived.
We revisit the problem of the deformed oscillator with position-dependent mass [da Costa et al., J. Math. Phys. {\bf 62}, 092101 (2021)] in the classical and quantum formalisms, by introducing the effect of the mass function in both kinetic…
We apply the Poisson sum rule to obtain formal expressions for the Fourier coefficients of the potential of a lattice of generalized charge. Each generalized charge is assumed to contribute to the potential a term which depends only on the…
A matrix representation of the evolution operator associated with a nonlinear stochastic flow with additive noise is used to compute its spectrum. In the weak noise limit a perturbative expansion for the spectrum is formulated in terms of…
The three dimensional harmonic oscillator model including a cranking term is used for an energy variational calculation. Energy minima are found under variation of the three oscillator frequencies determining the shape of the system for…
We consider a product of an arbitrary number of independent rectangular Gaussian random matrices. We derive the mean densities of its eigenvalues and singular values in the thermodynamic limit, eventually verified numerically. These…
This paper studies the asymptotic spectral properties of the sample covariance matrix for high dimensional compositional data, including the limiting spectral distribution, the limit of extreme eigenvalues, and the central limit theorem for…
The impedance matrix method is applied to study the scattering of flexural waves propagating in an infinite thin plate containing an $N$-beam resonator. The resonator consists of a circular hole containing a smaller plate connected to the…