Quantum solution of coupled harmonic oscillator systems beyond normal coordinates
作者: José ZúñigaAdolfo BastidaAlberto Requena
作者单位: 1Universidad de Murcia
刊名: Journal of Mathematical Chemistry, 2017, Vol.55 (10), pp.1964-1984
来源数据库: Springer Journal
DOI: 10.1007/s10910-017-0777-1
关键词: Coupled harmonic oscillatorsNormal coordinatesNon-orthogonal linear coordinatesBarbanis oscillator systemQuantum treatment
英文摘要: Normal coordinates can be defined as orthogonal linear combinations of coordinates that remove the second order couplings in coupled harmonic oscillator systems. In this paper we go further and explore the possibility of using linear although non-orthogonal coordinate transformations to get the quantum solution of coupled systems. The idea is to use as non-orthogonal linear coordinates those which allow us to express the second-order Hamiltonian matrix in a block diagonal form. To illustrate the viability of this treatment, we first apply it to a system of two bilinearly coupled harmonic oscillators which admits analytical exact solutions. The method provides in this case, as an extra mathematical result, the analytical expressions for the eigenvalues of a certain type of symmetrical...
原始语种摘要: Normal coordinates can be defined as orthogonal linear combinations of coordinates that remove the second order couplings in coupled harmonic oscillator systems. In this paper we go further and explore the possibility of using linear although non-orthogonal coordinate transformations to get the quantum solution of coupled systems. The idea is to use as non-orthogonal linear coordinates those which allow us to express the second-order Hamiltonian matrix in a block diagonal form. To illustrate the viability of this treatment, we first apply it to a system of two bilinearly coupled harmonic oscillators which admits analytical exact solutions. The method provides in this case, as an extra mathematical result, the analytical expressions for the eigenvalues of a certain type of symmetrical...
全文获取路径: Springer  (合作)
分享到:
来源刊物:
影响因子:1.226 (2012)

×
关键词翻译
关键词翻译
  • coordinates 坐标
  • coupled 耦合
  • oscillator 振荡器
  • harmonic 谐波
  • diagonal 对角线
  • demonstrate 说明
  • efficient 有用的
  • mathematical 数学的
  • linear 线形的
  • orthogonal 直交的