On the algebraic approach to the time-dependent quadratic Hamiltonian

被引:2
|
作者
Urdaneta, Ines [1 ]
Sandoval, Lourdes [2 ]
Palma, Alejandro [1 ]
机构
[1] Benemerita Univ Autonoma Puebla, Inst Fis, Puebla, Mexico
[2] Benemerita Univ Autonoma Puebla, Fac Ciencias Computac, Puebla, Mexico
关键词
COHERENT STATES; OPERATOR;
D O I
10.1088/1751-8113/43/38/385204
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
The unitary operator V (t) that diagonalizes the time-dependent quadratic Hamiltonian (TDQH) into a time-dependent harmonic oscillator (TDHO) is obtained using a Lie algebra. The method involves a factorization of the TDQH into a TDHO through a unitary Bogoliubov transformation in terms of creation and annihilation operators with time-dependent coefficients. It is shown that this operator can be easily achieved by means of the factorization, together with the commonly known Wei-Norman theorem. We discuss the conditions under which this unitary operator converges to the evolution operator U(t) of the Schrodinger equation for the TDQH, giving then a straightforward calculation of the evolution operator with respect to the procedures published in the literature.
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页数:10
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