相关论文: Exact solution and perturbation theory in a genera…
The construction of exactly-solvable models has recently been advanced by considering integrable $T\bar{T}$ deformations and related Hamiltonian deformations in quantum mechanics. We introduce a broader class of non-Hermitian Hamiltonian…
Using the Hubbard representation for $SU(2)$ we write the time-evolution operator of a two-level system in the disentangled form. This allows us to map the corresponding dynamical law into a set of non-linear coupled equations. In order to…
We significantly enhance the simulation accuracy of initial Trotter circuits for Hamiltonian simulation of quantum systems by integrating first-order Riemannian optimization with tensor network methods. Unlike previous approaches, our…
Within the frame of a novel treatment we make a complete mathematical analysis of exactly solvable one-dimensional quantum systems with non-constant mass, involving their ordering ambiguities. This work extends the results recently reported…
This report addresses the boundary value problem for a second-order linear singularly perturbed FIDE. Traditional methods for solving these equations often face stability issues when dealing with small perturbation parameters. We propose an…
Hamiltonian truncation is a non-perturbative numerical method for calculating observables of a quantum field theory. The starting point for this method is to truncate the interacting Hamiltonian to a finite-dimensional space of states…
Transport phenomena play a vital role in various fields of science and engineering. In this work, exact solutions are derived for advection equations with integer- and fractional-order time derivatives and a constant time-delay in the…
An exact invariant is derived for three-dimensional Hamiltonian systems of $N$ particles confined within a general velocity-independent potential. The invariant is found to contain a time-dependent function $f_{2}(t)$, embodying a solution…
We derive a rigorous, quantum mechanical map of fermionic creation and annihilation operators to continuous Cartesian variables that exactly reproduces the matrix structure of the many-fermion problem. We show how our scheme can be used to…
Accurate theoretical data on many time-dependent processes in atomic and molecular physics and in chemistry require the direct numerical solution of the time-dependent Schr\"odinger equation, thereby motivating the development of very…
Perturbation theory is an important technique for reducing computational cost and providing physical insights in simulating quantum systems with classical computers. Here, we provide a quantum algorithm to obtain perturbative energies on…
In the q-deformed theory the perturbation approach can be expressed in terms of two pairs of undeformed position and momentum operators. There are two configuration spaces. Correspondingly there are two q-perturbation Hamiltonians, one…
The Legendre transform expresses dynamics of a classical system through first-order Hamiltonian equations. We consider coherent state transforms with a similar effect in quantum mechanics: they reduce certain quantum Hamiltonians to…
We analyse the exact solutions of a conditionally-solvable Schr\"odinger equation with a rational potential. From the nodes of the exact eigenfunctions we derive a connection between the otherwise isolated exact eigenvalues and the actual…
We discuss a new analytical approach to real-time evolution in quantum many-body systems. Our approach extends the framework of continuous unitary transformations such that it amounts to a novel solution method for the Heisenberg equations…
By exploiting the hidden algebraic structure of the Schrodinger Hamiltonian, namely the sl(2), we propose a unified approach of generating both exactly solvable and quasi-exactly solvable quantum potentials. We obtain, in this way, two new…
This paper describes a new numerical method for solving eigenstate problems, such as time-independent Schrodinger equation. The idea is to use the first order perturbation theory to rewrite the eigenvalue problem as a system of first order…
An exact solution of the energy shift in each quantum mechanical energy levels in a one dimensional symmetrical linear harmonic oscillator has been investigated. The solution we have used here is firstly derived by manipulating Schrodinger…
A new approach in solution of simple quantum mechanical problems in deformed space with minimal length is presented. We propose the generalization of Schro\"edinger equation in momentum representation on the case of deformed Heisenberg…
Brief introduction to the discrete quantum mechanics is given together with the main results on various exactly solvable systems. Namely, the intertwining relations, shape invariance, Heisenberg operator solutions, annihilation/creation…