Related papers: Analytic Solution of Ground State for Coulomb Plus…
We investigate within the formalism of Symplectic Quantum Mechanics a two-dimensional non-relativistic strong interacting system that represents the bound heavy quark-antiquark state, where it was considered a linear potential in the…
A numerical method of solving the one-dimensional Schrodinger equation for the regular and irregular continuum states using the phase-amplitude representation is presented. Our solution acquires the correct Dirac-delta normalization by…
The Schr\"odinger-like equation written in terms of the displacement operator is solved analytically for a inverse square plus Coulomb-like potential. Starting from the new Hamiltonian, the effects of the spatially dependent mass on the…
We focus on a recently developed generalized pseudospectral method for accurate, efficient treatment of certain central potentials of interest in various branches in quantum mechanics, usually having singularity. Essentially this allows…
The higher dimensional quantum Hall liquid constructed recently supports stable topological membrane excitations. Here we introduce a microscopic interacting Hamiltonian and present its exact ground state wave function. We show that this…
The Wheeler-DeWitt equation is investigated and used to examine a state after a quantum tunneling with gravity. To make arguments definite we treat a discretized version of the Wheeler-DeWitt equation and adopt the WKB method. We expand an…
We address the problem of constructing a non-equilibrium stationary state for a one-dimensional stochastic Klein-Gordon wave equation with non-linearity, using perturbation theory. The linear theory is reviewed, but with the linear…
Qubits of long coherence time and fast quantum operations are long-sought objectives towards the realization of high-fidelity quantum operations and their applications to the quantum technologies. An electron levitated in a vacuum by a Paul…
A novel soliton-like solution in quantum electrodynamics is obtained via a self-consistent field method. By writing the Hamiltonian of quantum electrodynamics in the Coulomb gauge, we separate out a classical component in the density…
We consider energy-critical damped wave equation \begin{equation*} \partial_{tt}u-\Delta u+\alpha \partial_t u=\left|u\right|^{\frac{4}{D-2}}u \end{equation*} with radial initial data in dimensions $D\geq 4$. The equation has a nontrivial…
Eigenstates of the FQHE hamiltonian problem after to be projected on the LLL are determined for filling factors 1/q, with q an odd number. The solutions are found for an infinite class of finite samples in which the Coulomb potential is…
The problem of finding the ground state energy of a Hamiltonian using a quantum computer is currently solved using either the quantum phase estimation (QPE) or variational quantum eigensolver (VQE) algorithms. For precision $\epsilon$, QPE…
The preparation of the ground state of a Hamiltonian $H$ with a large spectral radius has applications in many areas such as electronic structure theory and quantum field theory. Given an initial state with a constant overlap with the…
We provide some new results of the ground state of quantum layers.
Wavefunctions for large electron numbers $N$ are plagued by the Exponential Wall Problem (EWP), i.e., an exponential increase in the dimensions of Hilbert space with $N$. Therefore they loose their meaning for macroscopic systems, a point…
The ordinary Landau problem of a charged particle in a plane subjected to a perpendicular homogeneous and static magnetic field is reconsidered from different points of view. The role of phase space canonical transformations and their…
Obtaining the total wavefunction evolution of interacting quantum systems provides access to important properties, such as entanglement, shedding light on fundamental aspects, e.g. quantum energetics and thermodynamics, and guiding towards…
A more reasonable trial ground state wave function is constructed for the relative motion of an interacting two-fermion system in a 1D harmonic potential. At the boundaries both the wave function and its first derivative are continuous and…
The recently developed quadrature by expansion (QBX) technique accurately evaluates the layer potentials with singular, weakly or nearly singular, or even hyper singular kernels in the integral equation reformulations of partial…
The method reducing the solution of the Schroedinger equation for several types of power potentials to the solution of the eigenvalue problem for the infinite system of algebraic equations is developed. The finite truncation of this system…