衡阳师范学院学报
衡暘師範學院學報
형양사범학원학보
JOURNAL OF HENGYANG NORMAL UNIVERSITY
2012年
3期
61-64
,共4页
唐世清%汪新文%何明智%张登玉%高峰
唐世清%汪新文%何明智%張登玉%高峰
당세청%왕신문%하명지%장등옥%고봉
共同本征函数系%算符对易%交集法%线性组合法
共同本徵函數繫%算符對易%交集法%線性組閤法
공동본정함수계%산부대역%교집법%선성조합법
simultanious eigenfunctions%commutation%intersection method%linear combination method
算符理论是量子力学课程的重要教学内容,其中两个力学量算符的对易及其本征函数问题是算符理论中的一个难点。简并情况下两个对易算符的本征函数系问题更为复杂,很多传统教材中都没有进行详细分析和讨论。该文利用一种简单的方法证明了简并情况下两个对易算符具有共同本征函数系的结论,并提出了寻找两个对易算符的共同本征函数系的两种简单方法—交集法与线性组合法。该文有助于教师和学生深刻地领会和求解两个对易算符的共同本征函数问题。
算符理論是量子力學課程的重要教學內容,其中兩箇力學量算符的對易及其本徵函數問題是算符理論中的一箇難點。簡併情況下兩箇對易算符的本徵函數繫問題更為複雜,很多傳統教材中都沒有進行詳細分析和討論。該文利用一種簡單的方法證明瞭簡併情況下兩箇對易算符具有共同本徵函數繫的結論,併提齣瞭尋找兩箇對易算符的共同本徵函數繫的兩種簡單方法—交集法與線性組閤法。該文有助于教師和學生深刻地領會和求解兩箇對易算符的共同本徵函數問題。
산부이론시양자역학과정적중요교학내용,기중량개역학량산부적대역급기본정함수문제시산부이론중적일개난점。간병정황하량개대역산부적본정함수계문제경위복잡,흔다전통교재중도몰유진행상세분석화토론。해문이용일충간단적방법증명료간병정황하량개대역산부구유공동본정함수계적결론,병제출료심조량개대역산부적공동본정함수계적량충간단방법—교집법여선성조합법。해문유조우교사화학생심각지령회화구해량개대역산부적공동본정함수문제。
The operator theory is a very important part in the quantum mechanics, in which two mechanical quantity operator commutative problem and their simultanious eigenfunctions are difficult points in the operator theory as they are more complex especially in degenerate situation. Moreover, detailed analysis and discussion is not given in many traditional textbooks. In this paper, a simple proof that two commutative operators can hold the simultanious eigenfunctions in degenerate situation is pres- ented, and we propose two simple methods to solve simultanious eigenfunetions of two commutative operators in degenerate sit uation: the intersection method and the linear combination method. This can help teachers and students deeply understand and solve the problems of the simultanious eigenfunctions of two commutative operators.