Related papers: Numerical matrix method for quantum periodic poten…
The paper considers the numerical solution of nonlinear integral equations using the Newton-Kantorovich method with the mpmath library. High-precision quadrature of the kernel K(t, s, u) with respect to the variable s for fixed t increases…
Recently, a novel bootstrap method for numerical calculations in matrix models and quantum mechanical systems is proposed. We apply the method to certain quantum mechanical systems derived from some well-known local toric Calabi-Yau…
Quantum computing has attracted significant interest in the optimization community because it potentially can solve classes of optimization problems faster than conventional supercomputers. Several researchers proposed quantum computing…
A continuous-time path integral Quantum Monte Carlo method using the directed-loop algorithm is developed to simulate the Anderson single-impurity model in the occupation number basis. Although the method suffers from a sign problem at low…
We develop a systematic procedure for constructing quantum many-body problems whose spectrum can be partially or totally computed by purely algebraic means. The exactly-solvable models include rational and hyperbolic potentials related to…
Consider the interaction of biharmonic waves with a periodic array of cavities, characterized by the Kirchhoff--Love model. This paper investigates the perfectly matched layer (PML) formulation and its numerical soution to the governing…
We consider the problem of defining quantum integrability in systems with finite number of energy levels starting from commuting matrices and construct new general classes of such matrix models with a given number of commuting partners. We…
A combined method for analyzing quantum dynamical equations which uses the Bohmian mechanics and the quantum phase space representation is proposed. It is based on a presentation of the wave function in phase space in a polar form. The…
We introduce a method to numerically compute equilibrium measures for problems with attractive-repulsive power law kernels of the form $K(x-y) = \frac{|x-y|^\alpha}{\alpha}-\frac{|x-y|^\beta}{\beta}$ using recursively generated banded and…
We study the effectiveness of the numerical bootstrap techniques recently developed in arXiv:2004.10212 for quantum mechanical systems. We find that for a double well potential the bootstrap method correctly captures non-perturbative…
In order to formulate mathematical conjectures likely to be true, a number of base cases must be determined. However, many combinatorial problems are NP-hard and the computational complexity makes this research approach difficult using a…
Quantum signal processing (QSP) provides a representation of scalar polynomials of degree $d$ as products of matrices in $\mathrm{SU}(2)$, parameterized by $(d+1)$ real numbers known as phase factors. QSP is the mathematical foundation of…
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 unified approach, for solving a wide class of single and many-body quantum problems, commonly encountered in literature is developed based on a recently proposed method for finding solutions of linear differential equations. Apart from…
This article presents the first complete application of a quantum time-marching algorithm for simulating multidimensional linear transport phenomena with arbitrary boundaries, whereby the success probabilities are problem intrinsic. The…
We use projection methods to construct (global) quantum states with prescribed reduced (marginal) states, and possibly with some special properties such as having specific eigenvalues, having specific rank and extreme von Neumann or Renyi…
The one-dimensional infinite square well is the simplest solution of quantum mechanics, and consequently one of the most important. In this article, we provide this solution using the real Hilbert space approach to quaternic quantum…
Solving linear systems of equations is a common problem that arises both on its own and as a subroutine in more complex problems: given a matrix A and a vector b, find a vector x such that Ax=b. We consider the case where one doesn't need…
This paper is dedicated to an application of a quantum wave impedance approach for a study of infinite and semi-infinite periodic systems. Both a Dirac comb and a $\delta-\delta'$ comb as well as a Kronig-Penney model are considered. It was…
We show that supersymmetry is a simple but powerful tool to exactly solve quantum mechanics problems. Here, the supersymmetric approach is used to analyse a quantum system with periodic P\"oschl-Teller potential, and to find out the exact…