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Setting Limits on Supersymmetry Using Simplified Models

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Born-oppenheimer approximation near level crossing

Gordon¹, Avron

¹Department of Physics, Technion, 32000 Haifa, Israel.

Physical Review Letters

|September 16, 2000

Summary

This summary is machine-generated.

We describe wave functions near conical intersections using generalized hypergeometric functions. This provides a new mathematical tool for understanding molecular behavior, analogous to Airy functions for classical turning points.

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Area of Science:

Quantum Chemistry
Theoretical Physics
Mathematical Physics

Background:

The Born-Oppenheimer approximation is fundamental in molecular quantum mechanics.
Conical intersections are critical points where electronic states become degenerate.
Understanding wave functions near these intersections is crucial for reaction dynamics.

Purpose of the Study:

To analyze the Born-Oppenheimer problem near conical intersections in two dimensions.
To identify the mathematical functions describing wave functions at energies near the crossing energy.
To apply these findings to calculate the anomalous Zeeman shift in vibrational levels.

Main Methods:

Solving the Born-Oppenheimer equation near an isotropic conical intersection.
Relating the wave function to generalized hypergeometric functions (specifically 0F3).
Calculating the anomalous Zeeman shift for vibrational energy levels.

Main Results:

The wave function near an isotropic conical intersection is described by generalized hypergeometric functions 0F3.
This hypergeometric function serves as a conical intersection analog to the Airy function for classical turning points.
The anomalous Zeeman shift of vibrational levels near the crossing was calculated.

Conclusions:

Generalized hypergeometric functions provide a powerful mathematical framework for describing wave functions near conical intersections.
This work establishes a new theoretical tool for studying molecular systems with conical intersections.
The application to anomalous Zeeman shift demonstrates the practical utility of this approach in quantum chemistry.