Flow equation approach to diagonal representation of an unbounded Hamiltonian with complex eigenvalues

An approximate diagonalization method for large scale Hamiltonians

An approximate diagonalization method is proposed that combines exact diagonalization and perturbation expansion to calculate low energy eigenvalues and eigenfunctions of a Hamiltonian. The method involves deriving an effective Hamiltonian for each eigenvalue to be calculated, using perturbation expansion, and extracting the eigenvalue from the diagonalization of the effective Hamiltonian. The size of the effective Hamiltonian can be significantly smaller than that of the original Hamiltonian, hence the diagonalization can be done much faster. We compare the results of our method with those ob…

无界算子的特征值渐近性。双光子量子 Rabi 模型

Eigenvalues asymptotics of unbounded operators. Two-photon quantum Rabi model

本文研究无界算子在紧、相对紧及非紧等扰动下的特征值渐近性，推广 Janas-Naboko 引理，并以双光子量子 Rabi 模型为例给出能量算子大特征值三项渐近公式及相关多项式渐近性。

Short proofs of theorems of Mirsky and Horn on diagonals and eigenvalues of matrices

A theorem of Mirsky provides necessary and sufficient conditions for the existence of an N-square complex matrix with prescribed diagonal entries and prescribed eigenvalues. We give a simple inductive proof of this theorem.

谐振子型和库仑型势的三维本征值来自一维广义莫尔斯势：基于广义拉盖尔多项式的微扰分析

Three-Dimensional Eigenvalues of Harmonic Oscillator- and Coulomb-type Potentials from One-Dimensional Generalized Morse Potential: Perturbative Analyse based on Generalized Laguerre Polynomials

本文利用一维广义莫尔斯势的相似性，通过朗格变换和广义拉盖尔多项式的递推关系，微扰计算了库仑型和谐振子型势的三维能量本征值至二阶。

Spectrum of One-Dimensional Anharmonic Oscillators

We use a power-series expansion to calculate the eigenvalues of anharmonic oscillators bounded by two infinite walls. We show that for large finite values of the separation of the walls, the calculated eigenvalues are of the same high accuracy as the values recently obtained for the unbounded case by the inner-product quantization method. We also apply our method to the Morse potential. The eigenvalues obtained in this case are in excellent agreement with the exact values for the unbounded Morse potential.

具有正特征值的轴对称矩阵特征值问题的动力系统

Dynamical systems for eigenvalue problems of axisymmetric matrices with positive eigenvalues

针对具特殊结构的轴对称矩阵特征值问题，提出S-Oja-Brockett动力系统方程，证明其可全局收敛至矩阵的特征值与对应特征向量。