From the definition of the standard Perelomov coherent states we introduce the Perelomov number coherent states for any su(2) Lie algebra. With the displacement operator we apply a similarity transformation to the su(...From the definition of the standard Perelomov coherent states we introduce the Perelomov number coherent states for any su(2) Lie algebra. With the displacement operator we apply a similarity transformation to the su(2)generators and construct a new set of operators which also close the su(2) Lie algebra, being the Perelomov number coherent states the new basis for its unitary irreducible representation. We apply our results to obtain the energy spectrum, the eigenstates and the partition function of two coupled oscillators. We show that the eigenstates of two coupled oscillators are the SU(2) Perelomov number coherent states of the two-dimensional harmonic oscillator with an appropriate choice of the coherent state parameters.展开更多
We show that the（2＋1）-dimensional Dirac-Moshinsky oscillator coupled to an externa/ magnetic field can be treated algebraically with the SU（1,1） group theory and its group basis.We use the su（1,1） irreducible r...We show that the（2＋1）-dimensional Dirac-Moshinsky oscillator coupled to an externa/ magnetic field can be treated algebraically with the SU（1,1） group theory and its group basis.We use the su（1,1） irreducible representation theory to find the energy spectrum and the eigenfunctions.Also,with the su（1,1） group basis we construct the relativistic coherent states in a closed form for this problem.展开更多
基金Supported by SNI-México,COFAA-IPN,EDD-IPN,EDI-IPN,SIP-IPN Project No.20150935
文摘From the definition of the standard Perelomov coherent states we introduce the Perelomov number coherent states for any su(2) Lie algebra. With the displacement operator we apply a similarity transformation to the su(2)generators and construct a new set of operators which also close the su(2) Lie algebra, being the Perelomov number coherent states the new basis for its unitary irreducible representation. We apply our results to obtain the energy spectrum, the eigenstates and the partition function of two coupled oscillators. We show that the eigenstates of two coupled oscillators are the SU(2) Perelomov number coherent states of the two-dimensional harmonic oscillator with an appropriate choice of the coherent state parameters.
基金Supported by SNI-Mexico,COFAA-IPN,EDI-IPN,EDD-IPN,SIP-IPN project number 20140598
文摘We show that the（2＋1）-dimensional Dirac-Moshinsky oscillator coupled to an externa/ magnetic field can be treated algebraically with the SU（1,1） group theory and its group basis.We use the su（1,1） irreducible representation theory to find the energy spectrum and the eigenfunctions.Also,with the su（1,1） group basis we construct the relativistic coherent states in a closed form for this problem.
