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

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In summary, the conversation is about numerically solving the rotational Schrodinger equation for a molecule in an external potential, seeking advice or references for an easy derivation of the kinetic energy operator and determining if the solution is analytic for a general asymmetric top. The topic is covered in many books on molecular physics, such as W. Demtröder's Molecular Physics."
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christianjb
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Hi,
I'm looking to numerically solve the rotational Schrodinger 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.
 
Physics news on Phys.org

1. What is a rigid rotor?

A rigid rotor is a model used in physics and chemistry to describe the motion of a molecule. It assumes that the molecule is a rigid, non-deformable object and only considers its rotational motion.

2. What is an asymmetric top?

An asymmetric top is a type of rigid rotor where the moments of inertia along each of the three axes are different. This means that the molecule does not rotate around a single axis, but rather has a complex rotational motion.

3. How do you solve for S.E. (Schrodinger Equation) for a rigid rotor?

The Schrodinger Equation for a rigid rotor involves solving a second-order differential equation using the Hamiltonian operator. This can be done analytically or numerically using various methods such as the perturbation method or the variational method.

4. What is the significance of solving for S.E. for a rigid rotor?

Solving for the Schrodinger Equation for a rigid rotor allows us to determine the energy levels and corresponding wavefunctions of a molecule. This information is important in understanding the rotational properties and behavior of molecules, which has many applications in chemistry and physics.

5. Are there any simplifications or assumptions made when solving for S.E. for a rigid rotor?

Yes, the rigid rotor model assumes that the molecule is a perfect rigid body with no internal vibrations or deformations. It also neglects any external forces acting on the molecule, such as electric or magnetic fields. Additionally, the model assumes that the molecule is in a vacuum and not influenced by any surrounding particles or molecules.

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