Solving S.E. for rigid rotor (asymmetric top)

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SUMMARY

This discussion focuses on numerically solving the rotational Schrödinger equation for a rigid rotor treated as an asymmetric top in an external potential. The user seeks advice on deriving the kinetic energy operator, referencing the Wikipedia page on rigid rotors, which utilizes Euler angles. The inquiry also addresses the analyticity of the solution for general asymmetric tops and the potential formation of basis functions from free rotor solutions. Key literature mentioned includes W. Demtröder's "Molecular Physics."

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  • Understanding of the rotational Schrödinger equation
  • Familiarity with rigid rotor models in quantum mechanics
  • Knowledge of Euler angles and their application in physics
  • Basic concepts of molecular physics and external potentials
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  • Research the derivation of the kinetic energy operator for rigid rotors
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christianjb
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Hi,
I'm looking to numerically solve the rotational Schrödinger eqn. for a molecule which I'm happy to treat as an internally rigid body.

The molecule will be in an external potential, so it's not a free rotor.

Does anyone have any advice or references for an easy derivation of
the K.E. operator? The rigid rotor page on Wikipedia has a derivation in terms of Euler angles, which I can maybe just about follow. Is this a good way to do this problem?

Also, is the solution analytic for the general asymmetric top? If so- I'd like to form basis functions from the free rotor solutions.

Thanks in advance for any help.
 
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