一维δ函数势场中的谐振子

1维δ函数势场中的谐振子
 
摘要: 本文研究了1维δ势场中的谐振子的能量本征值及其本征波函数，并与1维谐振子的能量本征值和波函数进行了比较，分析了它们的性质不同的原因以及取不同势参数Z值时对偶宇称能量本征值和波函数的不同影响。针对1维δ势场中的谐振子的不同性质特征，尤其对于基态，着重研究了它的波函数和能级，作出了它的波函数和能级图像，并讨论了它的特殊性质及其应用前景。

关键词:  函数势；谐振子；波函数；能量本征值；应用。

Harmonic oscillator with a one-dimensional δ-function potential
 
Abstract: This thesis analyzes the energy eigenvalue and of the Harmonic oscillator with a one-dimensional δ-function, makes a comparative study of those of the one-dimensional harmonic oscillator, and analyzes the reason which causes their different quality and the different influences to the eigenvalue of the even parity energy and to the wave function when the number of the “Z” is different. According to the different features of the harmonic oscillator with a one-dimensional δ-function, especially to the ground state, it lays the stress on its wave function and energy class and works out their image to make an argumentation on their special quality and bright future of application.
 
Key words: δ-function; Harmonic oscillator; wave function; energy eigenvalue; application.
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