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.

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.

CASE STUDY OF THE CONVERGENCY OF NONLINEAR PERTURBATION SERIES: MORSE–FESHBACH NONLINEAR SERIES

1999 ◽  
Vol 14 (13) ◽  
pp. 2103-2115 ◽  
Author(s):  
BISWANATH RATH
Keyword(s):  
New York ◽  
Energy Levels ◽  
Perturbation Series ◽  
Nonlinear Perturbation ◽  
Theoretical Physics ◽  
The Matrix ◽  
Diagonalization Method ◽  
Matrix Diagonalization ◽  
Divergent Behavior

We study the divergent behavior of the Morse–Feshbach nonlinear perturbation series (MFNS) [P. M. Morse and H. Feshbach, Methods of Theoretical Physics, Part II (McGraw-Hill, New York, 1953)] for producing convergent energy levels using the ground state of a quartic anharmonic oscillator (AHO) in the strong coupling limit. Numerical calculations have been done up to tenth order. Further comparison of the MFNS convergent result has been made with the matrix diagonalization method.

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

Quantum chaos and statistical properties of energy levels for atom in parallel electric and magnetic fields

2015 ◽  
Vol 29 (35n36) ◽  
pp. 1550248
Author(s):  
Hai-Feng Yang ◽  
Yong-Gang Tan ◽  
Zhong-Li Liu ◽  
Hong-Zhi Fu
Keyword(s):  
Magnetic Fields ◽  
Quantum Chaos ◽  
Chaotic Dynamics ◽  
Nearest Neighbor ◽  
Energy Levels ◽  
Statistical Properties ◽  
The Core ◽  
Ideal System ◽  
Electric And Magnetic Fields ◽  
Diagonalization Method

In this paper, the statistical properties of energy levels are studied numerically for atom in parallel electric and magnetic fields, which is an ideal system to examine the contributions of external fields and ionic core to quantum chaos. The Stark maps of diamagnetic spectra and nearest neighbor spacing (NNS) distributions are obtained by diagonalization method incorporating core effect. We identify obvious level anti-crossing and large value of [Formula: see text] for barium, indicating that core effect has predominant contribution to chaotic dynamics in barium. To study the core effect in detail, we sweep the quantum defect artificially and find that larger core effect will undoubtedly induce stronger chaotic dynamics.

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