1S0态类氢原子能谱的相对论修正

论文总字数：14501字

摘 要

在本科阶段我们所学习的量子力学中，方程是非相对论的，其无法满足协变性要求。但在高能领域，微观粒子的运动速度非常高甚至可以达到光速，因此其相对论效应极其显著。而且在高能领域，存在粒子的产生和湮灭，而非相对论性量子力学中的方程是粒子数守恒。因此，在研究高能领域时应该用相对论性量子场论来描述。本文主要研究的是二粒子体系在态中势能的相对论修正。因此，本文将对描述二粒子体系的BS方程进行三维约化，并求出相应的方程势能的相对论修正。

首先明确BS波函数是一个的矩阵形式，因此本文利用束缚态各自的对称性，将BS波函数写成若干个标量函数的特定组合。然后，本文将BS方程由四维约化到三维。在这个过程中我们主要采用的是瞬时近似。通过瞬时近似将BS方程中的核与波函数均约化成三维的，并得到相应的方程势能的相对论修正。其势能零阶为我们熟知的库伦势，而势能第一阶修正对应于Breit势，但不完全相同。因为，我们之后还将得到的已经进行相对论修正的势能与Breit势进行比计较，发现我们求得的结果与Breit势存在常系数的区别。

关键词：方程；BS方程；三维约化；瞬时近似；Breit势

Abstract

In the quantum mechanics we have learned in our undergraduate years, the Schrodinger equations are non-relativistic and cannot satisfy the requirement of degeneration. But in the high energy field, the microscopic particles are extremely fast and even reach the speed of light. The relativistic effect is very obvious.And at high energies, there is the creation and annihilation of particles, and the Schrodinger equation in nonrelativistic quantum mechanics is the conservation of the number of particles.Therefore, we need to use the relativistic quantum field theory to go into the high energy field. So,we study the relativistic correction of the potential energy of a two-particle system at 0 state. Therefore, the main purpose of this paper is to reduce the bethe-salpeter equation describing two-particle system in three dimensions, so as to obtain the relativistic correction of the corresponding Schrodinger equation potential energy.

Firstly, it is clear that the BS wave function is a matrix form of. Therefore, in this paper, the symmetry of the bound states is used to expand the BS wave function according to the basis, so as to obtain the scalar wave function. Then, the BS equation is reduced from four dimensions to three. In this process we mainly use the instantaneous approximation. The kernel and wave functions in BS equation are reduced to 3d by instantaneous approximation, and the relativistic correction of the potential energy of Schrodinger equation is obtained. The zero order potential energy is known as the coulomb potential, and the first order correction of the potential energy corresponds to the Breit potential, but is not identical.Because, we also will have the potential energy which already carried on the relativity correction and Breit potential to carry on the comparison calculation later, discovered that we obtain the result and Breit potential existence constant coefficient difference.

Key words: Schrodinger equation; BS equation; three-dimensional reduction; instantaneous approximation; Breit potential

目 录

摘要 Ⅰ

Abstract Ⅱ

第一章 绪论 1

1.1 引言 1

1.2 量子力学与方程 2

1.2.1 光量子假设 2

1.2.2 原子的量子论 2

1.2.3 de Broglie的物质波 2

1.2.4 量子力学的建立 2

1.2.5 方程 3

第二章 量子电动力学 4

2.1 QED的费曼规则 4

2.2 Bethe-Salpeter方程及其三维约化 5

第三章 二粒子体系（0 态）势能的相对论修正 7

3.1 BS方程在0 态下的三维约化 7

3.2 势能的相对论修正 14

3.3 修正后的势能与Breit势比较 17

3.4 结论 18

参考文献 20

致谢 21

1. 绪论

1.1引言

目前，对于氢原子和类氢原子（如μ介子氢）的实验测量精度很高，但实验测得的结果与理论计算却出现了偏差。理论上氢原子与μ介子氢的差别仅仅是将氢原子中的电子换成μ介子，也就是说将方程中的电子质量直接换成μ介子质量，就能够计算相应的量。但计算结果却与实验测量结果无法完全对应，只有改变薛定谔方程中的部分参数才能使得计算结果与实验测量结果相符。

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