南京师大学报（自然科学版）
南京師大學報（自然科學版）
남경사대학보（자연과학판）
JOURNAL OF NANJING NORMAL UNIVERSITY (NATURAL SCIENCE EDITION)
2010年
1期
48-51
,共4页
正则变换%动量本征矢%幺正算符%双模坐标耦合谐振子
正則變換%動量本徵矢%幺正算符%雙模坐標耦閤諧振子
정칙변환%동량본정시%요정산부%쌍모좌표우합해진자
canonical transformation%momentum eigenvector%unitary operator%double coordinate coupling harmonic oscillator
为了精确求解双模坐标耦合谐振子体系的动力学问题,利用动量本征矢在Fock表象中的表示构造不对称积分,找到了与经典正则变换对应的量子幺正算符.借助于动量表象的完备性条件,证明了该算符的幺正性及其变换特性.应用此量子幺正算符,精确求解了双模坐标耦合谐振子体系的动力学问题.
為瞭精確求解雙模坐標耦閤諧振子體繫的動力學問題,利用動量本徵矢在Fock錶象中的錶示構造不對稱積分,找到瞭與經典正則變換對應的量子幺正算符.藉助于動量錶象的完備性條件,證明瞭該算符的幺正性及其變換特性.應用此量子幺正算符,精確求解瞭雙模坐標耦閤諧振子體繫的動力學問題.
위료정학구해쌍모좌표우합해진자체계적동역학문제,이용동량본정시재Fock표상중적표시구조불대칭적분,조도료여경전정칙변환대응적양자요정산부.차조우동량표상적완비성조건,증명료해산부적요정성급기변환특성.응용차양자요정산부,정학구해료쌍모좌표우합해진자체계적동역학문제.
In order to solve exactly the dynamic problems of the double coordinate coupling harmonic oscillators, the quantum unitary operator corresponding with classical canonical transformation is derived using the momentum eigenvector in Fock representation by constructing asymmetric integration. The unitarity and transformation properties of the operator are analyzed by virtue of completeness of momentum representation. The dynamic problems of the double coordinate coupling harmonic oscillators are solved exactly by using the operator.
