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Comparison between phase space structures in coupled Morse systems and in various su(2) approximations.

C. Jung¹, E. Ziemniak, M. Carvajal

¹Universidad Nacional Autonoma de Mexico, Centro de Ciencias Fisicas Apdo. postal 48-3, 62251 Cuernavaca, MexicoCentro Internacional de Ciencias, Cuernavaca, Mexico.

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|June 5, 2003

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Researchers explored transforming classical Hamiltonians into Lie algebra forms for quantum mechanics. Approximations preserving phase space structures were developed, illustrated using coupled Morse systems and the su(2) Lie algebra for molecular spectroscopy.

Area of Science:

Quantum mechanics
Mathematical physics
Molecular spectroscopy

Background:

Classical Hamiltonians in position and momentum offer clear system dynamics.
Lie algebra Hamiltonians simplify quantum mechanical treatments.
Exact transformations between these forms can be complex.

Purpose of the Study:

To develop methods for transforming classical Hamiltonians to Lie algebra representations.
To find approximations that maintain key system features during transformation.
To investigate the equality of classical phase space structures as a criterion for approximation.

Main Methods:

Approximation techniques for Hamiltonian transformation.
Analysis of classical phase space structures.

Related Experiment Videos

Application to coupled Morse systems.

Utilizing the su(2) Lie algebra.

Main Results:

Developed approximate transformations between classical and Lie algebra Hamiltonians.
Identified phase space structure equality as a key approximation criterion.
Demonstrated the approach for coupled Morse systems relevant to molecular spectroscopy.

Conclusions:

Approximate transformations are feasible and preserve essential quantum mechanical features.
The su(2) Lie algebra provides a useful framework for anharmonic molecular models.
This work facilitates the quantum mechanical analysis of complex systems.