用线性量子变换对角化二次型哈密顿量

刘汉俊; 逯怀新

量子电子学报, 2001, 18 (4): 324, 网络出版: 2006-05-15

用线性量子变换对角化二次型哈密顿量

Diagonalization of Quadratic Hamiltonian by the Linear Quantum Transformation

论文大纲

刘汉俊逯怀新

作者单位

昌潍师范专科学校物理系,潍坊,261043

二次型哈密顿量量子变换对角化 quadratic Hamiltonian quantum transformation diagonalization

摘要

借助线性量子变换(LQT)理论,对n模玻色和费米子的二次型哈密顿量,我们给出了简洁的对角化形式.并且指出,对于n模玻色子耦合二次型哈密顿量,通过一个负幺正矩阵(它是复辛群SP(2n,c)的元素)可以把它对角化;对n模费米子耦合二次型哈密顿量,通过一个幺正矩阵(它是复费米群F(2n,c)的元素)可以把它对角化.

Abstract

By the aid of the linear quantum transformation (LQT) theory,we give a concise diagonalization for n-mode boson and fermion of quadratic Hamiltonian. It is also pointed out that an n-mode boson coupled quadratic Hamiltonian can be diagonalized by a "negative unitary" matrix which is an element of complex symplectic group SP(2n,c),and an n-mode fermion coupled quadratic Hamiltonian can be diagonalized by a unitary matrix which is an element of complex fermion group F(2n,c).

参考文献

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刘汉俊, 逯怀新. 用线性量子变换对角化二次型哈密顿量[J]. 量子电子学报, 2001, 18(4): 324. 刘汉俊, 逯怀新. Diagonalization of Quadratic Hamiltonian by the Linear Quantum Transformation[J]. Chinese Journal of Quantum Electronics, 2001, 18(4): 324.

用线性量子变换对角化二次型哈密顿量

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