VIBRATIONAL SPECTRUM FOR THE LINEAR LATTICE CHAIN GAINED BY VIRTUE OF THE "INVARIANT EIGEN-OPERATOR" METHOD

2005 ◽  
Vol 19 (27) ◽  
pp. 4073-4080 ◽  
Author(s):  
HONG-YI FAN ◽  
HAO WU ◽  
XUE-FEN XU
Keyword(s):  
Boundary Condition ◽  
Vibrational Spectrum ◽  
Operator Method ◽  
Harmonic Oscillators ◽  
Linear Lattice ◽  
Coupled Harmonic Oscillators ◽  
Hamiltonian Models

We propose an operator Hamiltonian (a ring of identically coupled harmonic oscillators) to describe the linear lattice chain with Born–von Karmann boundary condition. We apply the method of "invariant eigen-operator" to study this Hamiltonian and derive its invariant eigen-operator. The vibrational spectrum is thus obtained. This approach seems concise and direct and can be extended to tackle other Hamiltonian models.

INVARIANT EIGEN-OPERATOR METHOD FOR SOLVING ENERGY GAP FOR SOME HAMILTONIANS IN MOLECULAR PHYSICS

2007 ◽  
Vol 21 (12) ◽  
pp. 1961-1969 ◽  
Author(s):  
HONG-YI FAN ◽  
TONG-TONG WANG
Keyword(s):  
Energy Gap ◽  
Molecular Model ◽  
Energy Levels ◽  
Linear Chain ◽  
Operator Method ◽  
Harmonic Oscillators ◽  
Molecular Physics ◽  
Coupled Harmonic Oscillators ◽  
Diagonalization Method

We show that the recently proposed invariant eigen-operator method is particularly applicable to solving the energy levels for some Hamiltonians in molecular physics. These are tri-atom molecules, the identical d-dimensional coupled harmonic oscillators and the dissipative linear-chain molecular model etc. The calculation is more direct and simpler than the usual diagonalization method for dynamic Hamiltonians.

Adaptive cluster synchronisation of coupled harmonic oscillators with multiple leaders

2013 ◽  
Vol 7 (5) ◽  
pp. 765-772 ◽  
Author(s):  
Housheng Su ◽  
Hongwei Wang ◽  
Michael Z. Q. Chen ◽  
Najl V. Valeyev ◽  
Xiaofan Wang
Keyword(s):  
Harmonic Oscillators ◽  
Coupled Harmonic Oscillators ◽  
Multiple Leaders

scholarly journals Group synchronization of diffusively coupled harmonic oscillators

Kybernetika ◽  
2016 ◽  
pp. 629-647 ◽  
Author(s):  
Liyun Zhao ◽  
Jun Liu ◽  
Lan Xiang ◽  
Jin Zhou
Keyword(s):  
Harmonic Oscillators ◽  
Coupled Harmonic Oscillators ◽  
Group Synchronization

Time-dependent coupled harmonic oscillators: Classical and quantum solutions

2014 ◽  
Vol 23 (09) ◽  
pp. 1450048 ◽  
Author(s):  
D. X. Macedo ◽  
I. Guedes
Keyword(s):  
Canonical Transformation ◽  
Unitary Transformation ◽  
Coupling Parameter ◽  
Wave Functions ◽  
Harmonic Oscillators ◽  
Time Dependent ◽  
Classical Solutions ◽  
Arbitrary System ◽  
Coupled Harmonic Oscillators ◽  
The Masses

In this work we present the classical and quantum solutions for an arbitrary system of time-dependent coupled harmonic oscillators, where the masses (m), frequencies (ω) and coupling parameter (k) are functions of time. To obtain the classical solutions, we use a coordinate and momentum transformations along with a canonical transformation to write the original Hamiltonian as the sum of two Hamiltonians of uncoupled harmonic oscillators with modified time-dependent frequencies and unitary masses. To obtain the exact quantum solutions we use a unitary transformation and the Lewis and Riesenfeld (LR) invariant method. The exact wave functions are obtained by solving the respective Milne–Pinney (MP) equation for each system. We obtain the solutions for the system with m1 = m2 = m0eγt, ω1 = ω01e-γt/2, ω2 = ω02e-γt/2 and k = k0.

Sign in / Sign up

Export Citation Format

Share Document