Related papers: Polynomial Approximations of Electronic Wave Funct…
This chapter discusses contemporary quantum chemical methods and provides general insights into modern electronic structure theory with a focus on heavy-element-containing compounds. We first give a short overview of relativistic…
Polaritonic chemistry is an interdisciplinary emerging field that presents several challenges and opportunities in chemistry, physics, and engineering. A systematic review of polaritonic response theory is presented, following a chemical…
New algebraic structure on electronic Fock space is studied in detail. This structure is defined in terms of a certain multiplication of many electron wave functions and has close interrelation with coupled cluster and similar approaches.…
We derive a set of Clifford-algebraic formulas for two major nonlinear conformal transformations of the physical quantities related to Maxwell's equations. The superiority of these formulas over their vector-tensorial counterparts are…
We propose models of quantum neural networks through Clifford algebras, which are capable of capturing geometric features of systems and to produce entanglement. Due to their representations in terms of Pauli matrices, the Clifford algebras…
In this paper we show how all the quantum properties of Schroedinger and Pauli particles can be described entirely from within a Clifford algebra taken over the reals. There is no need to appeal to any `wave function'. To describe a quantum…
Quantum theory (QT), namely in terms of Schr\"odinger's 1926 wave functions in general requires complex numbers to be formulated. However, it soon turned out to even require some hypercomplex algebra. Incorporating Special Relativity leads…
Coupled cluster theory produced arguably the most widely used high-accuracy computational quantum chemistry methods. Despite the approach's overall great computational success, its mathematical understanding is so far limited to results…
The structure of the nucleon wave function as a bound system of the constituent quarks was considered in framework of the quasipotential method of description of the bound states with a fixed number of particles. In the impulse…
In this article, we demonstrate the restricted Hartree-Fock electronic structure computation of the molecule $H_3^+$ through computational algebra. We approximate the Hartree-Fock total energy by a polynomial composed of LCAO coefficients…
We introduce an extended Kepler-Coulomb quantum model in spherical coordinates. The Schr\"{o}dinger equation of this Hamiltonian is solved in these coordinates and it is shown that the wave functions of the system can be expressed in terms…
We investigate the accuracy of a number of wavefunction based methods at the heart of quantum chemistry for metallic systems. Using Hartree-Fock as a reference, perturbative (M{\o}ller-Plesset, MP) and coupled cluster (CC) theories are used…
This paper concerns the notion of a symmetric algebra and its generalization to a quasi-symmetric algebra. We study the structure of these algebras in respect to their hull-kernel regularity and existence of some ideals, especially the…
The present survey results from the will to reconcile two approaches to quantum probabilities: one rather physical and coming directly from quantum mechanics, the other more algebraic. The second leading idea is to provide a unified picture…
Geometric Algebra and Calculus are mathematical languages encoding fundamental geometric relations that theories of physics seem to respect. We propose criteria given which statistics of expressions in geometric algebra are computable in…
Quantum computational chemistry is a potential application of quantum computers that is expected to effectively solve several quantum-chemistry problems, particularly the electronic structure problem. Quantum computational chemistry can be…
In our work we construct a Hamiltonian, whose eigenstates approximate the solutions of the self-consistent Hartree-Fock equations for nonrelativistic atoms and ions. Its eigenvalues are given by completely algebraic expressions and the…
We present a formulation of quantum mechanics based on orthogonal polynomials. The wavefunction is expanded over a complete set of square integrable basis in configuration space where the expansion coefficients are orthogonal polynomials in…
Various applications of quantum algebraic techniques in nuclear and molecular physics are briefly reviewed. Emphasis is put in the study of the symmetries of the anisotropic quantum harmonic oscillator with rational ratios of frequencies,…
Application of the so-called refined algebraic quantization scheme for constrained systems to the relativistic particle provides an inner product that defines a unique Fock representation for a scalar field in curved space-time. The…