Related papers: Simple variational approaches to quantum wells
This study examines Quaternion Dirac solutions for an infinite square well. The quaternion result does not recover the complex result within a particular limit. This raises the possibility that quaternionic quantum mechanics may not be…
It is classical that univariate algebraic functions satisfy linear differential equations with polynomial coefficients. Linear recurrences follow for the coefficients of their power series expansions. We show that the linear differential…
We study the partition function for the low-energy edge excitations of the incompressible electron fluid. On an annular geometry, these excitations have opposite chiralities on the two edges; thus, the partition function takes the standard…
Variational quantum algorithms are a promising tool for solving partial differential equations. The standard approach for its numerical solution are finite difference schemes, which can be reduced to the linear algebra problem. We consider…
We analyze qubit channels by exploiting the possibility of representing two-level quantum systems in terms of characteristic functions. To do so, we use functions of non-commuting variables (Grassmann variables), defined in terms of…
The role of differential equations (DEs) in science and engineering is of paramount importance, as they provide the mathematical framework for a multitude of natural phenomena. Since quantum computers promise significant advantages over…
We propose and analyse analogs of optical cavities for atoms using three-well inline Bose-Hubbard models with pumping and losses. With one well pumped and one damped, we find that both the mean-field dynamics and the quantum statistics show…
We derive analytical expressions for the correlation functions of the electronic conductance fluctuations of an open quantum dot under several conditions. Both the variation of energy and that of an external parameter such as an applied…
We present a framework for the analytic calculations of the hierarchical wave functions and the composite fermion wave functions in the fractional quantum Hall effect on the sphere by using projective coordinates. Then we calculate the…
We present a new hydrodynamic analogy of nonrelativistic quantum particles in potential wells. Similarities between a real variant of the Schr\"odinger equation and gravity-capillary shallow water waves are reported and analyzed. We show…
Quantum computing uses the physical principles of very small systems to develop computing platforms which can solve problems that are intractable on conventional supercomputers. There are challenges not only in building the required…
We present a solution of the quantum mechanics problem of the allowable energy levels of a bound particle in a one-dimensional finite square well. The method is a geometric-analytic technique utilizing the conformal mapping $w \to z = w…
This paper introduces variational design methods that are novel to Geophysics, and discusses their benefits and limitations in the context of geophysical applications and more established design methods. Variational methods rely on…
As an application of a recently developed variational perturbation theory we find the first 22 terms of the convergent strong-coupling series expansion for the ground state energy of the quartic anharmonic oscillator.
All quantum field theories that describe interacting bosonic elementary particles, share the feature that the zeroth order perturbation expansion describes non-interacting harmonic oscillators. This is explained in the paper. We then…
Eigenstates of a particle in a localized and unconfined harmonic potential well are investigated. Effects due to the variation of the potential parameters as well as certain results from asymptotic expansions are discussed.
Time analysis of oscillations of a particle between wells in the one-dimensional double-well potential with infinite high outside walls, based on wave packet use and energy spectrum analysis, is presented. For the double-well potential of…
The dynamics of a wave function describing a particle confined in a multiple quantum well potential is studied numerically. As a consequence of quantum mechanical tunneling, an initial wavefunction designed to be localized in one well can…
Trefftz methods are finite element-type schemes whose test and trial functions are (locally) solutions of the targeted differential equation. They are particularly popular for time-harmonic wave problems, as their trial spaces contain…
The variational quantum-classical algorithms are the most promising approach for achieving quantum advantage on near-term quantum simulators. Among these methods, the variational quantum eigensolver has attracted a lot of attention in…