相关论文: Bounds on Schr\"odinger Energies
Using Mathematica 3.0, the Schroedinger equation for bound states is solved. The method of solution is based on a numerical integration procedure together with convexity arguments and the nodal theorem for wave functions. The interaction…
In quantum theory, bound states are described by eigenvalue equations, which usually cannot be solved exactly. However, some simple general theorems allow to derive rigorous statements about the corresponding solutions, that is, energy…
The problem of quantum state preparation is one of the main challenges in achieving the quantum advantage. Furthermore, classically, for multi-level problems, our ability to solve the corresponding quantum optimal control problems is rather…
The purpose of this Comment is to show that the solutions to the zero energy Schr\"odinger equations for monomial central potentials discussed in a recently published Letter, may also be obtained from the corresponding free particle…
Three-body systems in two dimensions with zero-range interactions are considered for general masses and interaction strengths. The problem is formulated in momentum space and the numerical solution of the Schr\"odinger equation is used to…
This book considers posing and the methods of solving simple linear boundary-value problems in classical mathematical physics. The questions encompassed include: the fundamentals of calculus of variations; one-dimensional boundary-value…
We present an application of a nonstandard approximate method---the finite-rank approximation---to solving the time-independent Schr\"odinger equation for a bound-state problem. The method is illustrated on the example of a…
Standard variational methods tend to obtain upper bounds on the ground state energy of quantum many-body systems. Here we study a complementary method that determines lower bounds on the ground state energy in a systematic fashion, scales…
Variational methods play an important role in the study of quantum many-body problems, both in the flavor of classical variational principles based on tensor networks as well as of quantum variational principles in near-term quantum…
In this paper the problem of the gauge in a bound state calculation is discussed. In particular, in order to verify the gauge invariance in the energy levels expansion, some set of gauge invariant contributions are given.
The subjects which are discussed in this Thesis include: the self energy of a bound electron and the spin-dependence of QED corrections in bound systems, convergence acceleration techniques, and resummation methods for divergent series with…
We obtain the exact energy spectrum of nonuniform mass particles for a collection of Hamiltonians in a three-dimensional approach to a quantum dot. By considering a set of generalized Schr\"odinger equations with different orderings between…
One of the crucial properties of a quantum system is the existence of bound states. While the existence of eigenvalues below zero, i.e., below the essential spectrum, is well understood, the situation of zero energy bound states at the edge…
The quantum statistical treatment of the Rutherford model, considering matter as a system of point charges (electrons and nuclei) is analyzed. First, in the historical context, the solutions of different fundamental problems, such as the…
Methods for calculating lower bounds to the exact energy using the variance of the upper bound energy are discussed and explored. All the matrix elements of the Hamiltonian squared are collected and considered, and those for which no known…
The transfer-matrix methodology is used to solve linear systems of differential equations, such as those that arise when solving Schr\"odinger's equation, in situations where the solutions of interest are in the continuous part of the…
A general quantization rule for bound states of the Schrodinger equation is presented. Like fundamental theory of integral, our idea is mainly based on dividing the potential into many pieces, solving the Schr\"odinger equation, and…
It is shown that a class of approximate resonance solutions in the three-body problem under the Newtonian gravitational force are equivalent to quantized solutions of a modified Schr\"odinger equation for a wide range of masses that…
In the book the mathematical methods of nuclear cross sections and phases of elastic scattering, energy and characteristics of bound states in two- and three-particle nuclear systems, when the potentials of interaction contain not only…
We establish quantum dynamical lower bounds for a number of discrete one-dimensional Schr\"odinger operators. These dynamical bounds are derived from power-law upper bounds on the norms of transfer matrices. We develop further the approach…