New description for quantum motions of linear harmonic oscillator and q - deformed harmonic oscillator 變形振子量子運(yùn)動的新描述
Solution to the problems of one and two - dimensional linear harmonic oscillators by using operators 一維及二維線性諧振子的算符解法
For small displacement u , the oscillator is a duffing - type cubic non - linear oscillator , while for large displacement u , the oscillator approximates to a linear harmonic oscillator 所謂達(dá)芬諧波振子是指當(dāng)位移遠(yuǎn)小于1時,系統(tǒng)可化為三次非線性振子,而當(dāng)位移遠(yuǎn)大于1時,該系統(tǒng)則化為線性諧波振子。
There were troubles in the continuity of the function and of its - derivative divided by band - mass on the boundary . in the theoretical calculation , the wave function is relative to the physical properties of the impurity greatly , the envelop function f ( x , y ) is expanded in terms of the one - dimensional linear harmonic oscillator function in this paper . it satisfies the continuity of the function and of its - derivative divided by the band - mass , so it improves the precision of the function and binding energy 與以往工作不同的是,以前選用的x , y方向電子的包絡(luò)函數(shù)f ( x , y )是一維有限深量子阱中波函數(shù)的乘積,在邊界上波函數(shù)的連續(xù)性和粒子流的守恒條件存在問題;而在理論計算中,波函數(shù)的選取與雜質(zhì)的物理性質(zhì)有密切關(guān)系,本文選取的電子的包絡(luò)函數(shù)是用一維線性諧振子的波函數(shù)展開而成的,在邊界上能夠同時滿足波函數(shù)的連續(xù)性及粒子流( 1 / m ~ * ) f ' ( x , y )的守恒條件,從而使得波函數(shù)和束縛能的精確度得到了改進(jìn)。