一維δ函數勢場中的諧振子

1維δ函數勢場中的諧振子
 
摘要: 本文研究了1維δ勢場中的諧振子的能量本征值及其本征波函數，并與1維諧振子的能量本征值和波函數進行了比較，分析了它們的性質不同的原因以及取不同勢參數Z值時對偶宇稱能量本征值和波函數的不同影響。針對1維δ勢場中的諧振子的不同性質特征，尤其對于基態(tài)，著重研究了它的波函數和能級，作出了它的波函數和能級圖像，并討論了它的特殊性質及其應用前景。

關鍵詞:  函數勢；諧振子；波函數；能量本征值；應用。

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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