谐振子势中附加δ势后偶宇称态的近似解  

Approximate solutions of even parity stationary states in harmonic oscillator potential with δ potential added

作　　者：李明明[1] 陈岗[2] 

机构地区：[1]济南大学理学院,济南250022 [2]山东警察学院基础部,济南250101

出　　处：《大连海事大学学报》2009年第2期145-147,共3页Journal of Dalian Maritime University

摘　　要：为获得较为准确的基态能量,选用试探波函数来计算基态能量.在一维谐振子势中附加δ势后,原来的奇宇称定态解仍是解,而原来的偶宇称定态解不再是解.为此,分别用定态微扰论与变分法计算偶宇称定态的近似解,用变分法求解薛定谔方程,计算所得的偶宇称定态能量近似值与严格值吻合很好,特别在激发态,其相对误差小于10-3,且所有能级的能量近似值都大于严格值.结果表明,用定态微扰论或变分法计算谐振子势附加δ势后的偶宇称定态近似能量是简单可行的.Trial wave function was used to calculate ground state energy to obtain a relatively accurate value. After adding potential δ to one-dimensional harmonic oscillator, the odd parity stationary states of the harmonic oscillator still held and the even parity stationary states were no longer correct. Therefore, the perturbation theory and variational method were used respectively to calculate the approximate even parity stationary states, and variational method was used to solve Schrodinger equation. Results show that the calculated approximate even parity stationary states match well with the desired value, especially in excited state, the relative error is less than × 10^-3, and all the approximate values of energy for all levels are higher than desired value, which prove that it is simple and feasible by using perturbation theory or variational method to calculate approximate even parity stationary states with δ potential added.

关 键 词：谐振子 定态薛定谔方程 偶宇称 试探波函数 

分 类 号：O413.1[理学—理论物理]