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理论物理通讯：英文版

New Convenient Way for Disentangling Exponential Operator Composed of Angular Momentum Operators

Li, Hongqi, Xu, Xing-Lei, Fan, Hong-Yi

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

在前面的纸(Commun。Theor。Phys。51 (2009 ) 321 ) 我们为解开指数的操作员推荐了一个方便方法。在这个工作，我们使用这个方法解开由尖动量操作员组成的指数的操作员。我们主要解开 exp 的形式[ 2hJz +gJ++ kJ ]作为订的 exp (...J+) exp (... Jz ) exp (... J )，我们采用 Schwinger Bose 实现 J = ba ，J+= ab ， Jz =( aa bb )完成这项任务的 /2 ，没有呼吁谎言代数学方法。注意这个操作员的解开与它在正常的订的分解不同。

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A note on the angular momentum operators

A. Bose

American Journal of Physics•Oct 1, 1988•0 citations

A note on the angular momentum operators

P. T. Leung

American Journal of Physics•Dec 1, 1986•1 citation
在前面的纸(Commun。Theor。Phys。51 (2009 ) 321 ) 我们为解开指数的操作员推荐了一个方便方法。在这个工作，我们使用这个方法解开由尖动量操作员组成的指数的操作员。我们主要解开 exp 的形式[ 2hJz +gJ++ kJ ]作为订的 exp (...J+) exp (... Jz ) exp (... J )，我们采用 Schwinger Bose 实现 J = ba ，J+= ab ， Jz =( aa bb )完成这项任务的 /2 ，没有呼吁谎言代数学方法。注意这个操作员的解开与它在正常的订的分解不同。
In the preceding paper ( Commun. Theor. Phys. 51 (2009) 321 ) we have recommended a convenient method for disentangling exponential operators. In this work we use this method for disentangling exponential operators composed of angular momentum operators. We mainly disentangle the form of exp[2hJ z + gJ + + kJ − ] as the ordering exp(...J + )exp(...J z )exp(...J − ), we employ the Schwinger Bose realization J − = b † a, J + = a † b, J z = (a † a − b † b)/2 to fulfil this task, without appealing to Lie algebra method. Note that this operator's disentangling is different from its decomposition in normal ordering.
In the preceding paper [Commun. Theor. Phys. 51 (2009) 321] we have recommended a convenient method for disentangling exponential operators in the form of exp{B + C}, trying to find an operator A that satisfies [A, B] = C, and [A,[A,B]] = 0, then from the Baker–Hausdorff formula we have exp{B + C} = exp{B+[A, B]} = e A e B e −A . After arranging e A e B = e B e A e W , the disentangling exp{B + C} = e B e W is obtained. In this work we use this method to two-mode case, especially, derive the normal ordering form of exp[h(a † a + b † b) + ga † b † + kab] without appealing to Lie algebra method.