The Quantum Analysis For The Phase Space About The Coupling Charateristics Of The Triatomic Molecule

The common triatomic molecules such as ABA, ABC forms, they have a variety of different ways of coupling, such as linear model coupling and L coupling, etc. The linear coupling is mainly in the non-center symmetric linear triatomic molecule is given priority to, normal vibration modes including symmetric stretching vibration, antisymmetric stretching vibration and bending vibration, etc. The L type coupling are mainly composed of nonlinear triatomic molecules, normal vibration modes including symmetric stretching vibration and bending vibration and antisymmetric stretching vibration, etc. As the ABC type triatomic molecules with wider range of research in form, its characteristic is determined more by atomic itself, and do not have much in common. The ABA type triatomic molecules with symmetry in form, the ABA triatomic molecule has a similar vibration frequency, can produce resonance commonness, allowed the ABA type triatomic molecules coupling characteristics have important significance. In the research of the ABA type triatomic molecules, people usually use the classical theory of molecular physics analysis, although to a certain extent, explains the stability of the molecular level and spectrum distribution characteristics and so on, but there are still many problems need the quantum theory to explain, for example, quantum tunneling effect, etc. In this paper, based on the quadratic Hamiltonian of quantization, as the ABA triatomic molecules as the research subject, combined with the evolution equation of the levels and the stability of the some theories of the phase space, study the ABA triatomic molecules in change respectively 1:1 resonance coupling coefficient, to study the fidelity of the evolution about the coupling vibration levels, based on the Husimi distribution function, the different eigen states’ phase space distribution statistical properties of the ABA triatomic molecule and the phase space trajectory of the ABA triatomic molecules, etc.In the study class ABA triatomic molecule A-B key coupling vibration level stability, on the theories of the quadratic quantization Hamiltonian model, by changing the 1:1 resonance coupling coefficient,research the fidelity of the A-B keys coupling vibration about the ABA triatomic molecule level evolution, and determine its stability. The water molecules which is L type nonlinear triatomic molecules as the research model, combined with the second quantized Hamiltonian and related parameters of the water molecules, and get the image about the fidelity of the evolution over time. The results show that the different choice of initial state may affect the H2 O about the O-H keys in the stability of the level. 1. The original state of all or most of the energy focus on one key, then the energy level is stable; 2. The initial state is the middle state that is the two O-H keys have equal vibration strength, the coupling resonance is strong and its stability is weak. 3. When in the same initial state, the greater of the 1:1 resonance coupling coefficient change the weaker of the stability.This article on the basis of Husimi distribution function and further research about the water molecules phase space distribution. By analyze phase diagram found: at the high energy level, because of the two oscillators’ coupling is stronger, the phase angle between -pp),( relatively, which is show the normal model’s character; At the low level, due to the weak coupled of the two oscillators, the two phase angles is independent relatively, there is no constant relationship of the phase angle, to present local models’ character. In order to further study the characteristics of the phase space, by introducing position operator and momentum operator, combined with relevant Hamiltonian and parameter analysis, studies the phase space trajectory. The results show that at a higher level, the location of the vibration amplitude is not large, the momentum vibration amplitude is more than the locations’; With lower energy level, the phase space trajectory’s momentum fluctuation amplitude reduced, the vibration amplitude at the lower level may be changing. When the oscillator is in lowest level, the position of the phase space trajectory changes in volatility is very obviously, the change of momentum is relatively less. As the time goes on, the phase space trajectory should be oval structures in the classics. But, because of the coupling between the stator, under the quantum description, the phase space spiral shape trajectory form similar to the classical phase space trajectory, the phase space trajectory based on the classical corresponding oval structures and the spiral structure which is can’t be described by the classical way. Through respectively compared the momentums and the positions of the two vibrator, and found a linear relationship between them, the position of the two vibrator is synchronous change, which is similar to the classic symmetry vibration mode; But the momentum is a negative correlation, it also embodies the system’s momentum is conserved; After changing the 1:1 resonance coupling coefficient, that is the adding the disturbance)(21221aaaabb Lx+++= on the Hamilton H and found that: with the b changes, the momentum statistical distribution will be affected, in other words, change the 1:1 coupling coefficient will affect the fluctuation range of the momentum to the phase space trajectory.