# Spin Dynamics Forum

## SpinDynamica support => Simulations => Topic started by: johannes.mckay on July 02, 2012, 09:28:47 AM

Title: Cartesian interaction matrix into spherical tensor
Post by: johannes.mckay on July 02, 2012, 09:28:47 AM
Thanks for any help to this question(s)!

I am having a bit of trouble translating a cartesian interaction matrix into a spherical tensor, I have managed to do this by hand following the guide handed out by Ilya and using the tables of coefficients, but doing it in SpinDynamica leaves me a little bit lost. Are there any functions particularly suited to this operation, I didn't find anything in the usage examples but I might have missed them?

Cheers,
Johannes
Title: Re: Cartesian interaction matrix into spherical tensor
Post by: JyrkiRantaharju on July 02, 2012, 04:30:17 PM
I think you could use ExpressOperator[operator,SphericalTensorOperatorBasis[]]. Where operator should be opI["I"].Interaction_matrix.opI["S"] for an interaction matrix between spins I and S.
Title: Re: Cartesian interaction matrix into spherical tensor
Post by: johannes.mckay on July 02, 2012, 04:53:42 PM
Hi Jyrki, Having a quick scan of ?SphericalTensorOperatorBasis I think this is the generating function that I am missing. I will give this a go tonight and see how I get on. Thanks for the quick reply.

Cheers,
Johannes
Title: Re: Cartesian interaction matrix into spherical tensor
Post by: MalcolmHLevitt on July 26, 2012, 09:31:43 AM
Jyrki's reply does not quite do what you want, I think, since the spherical tensor operators will not be kept separate in the output.

I've attached a notebook which may help. This shows how a general bilinear product of two angular momentum operators may be represented as a vector in the SphericalTensorOperatorBasis, and also how the routine OperatorAmplitude may be used for the individual operators.
Title: Re: Cartesian interaction matrix into spherical tensor
Post by: johannes.mckay on July 26, 2012, 08:19:46 PM
Hi Malcolm

Cheers for the notebook, I am just looking at it just now. I will go back and revise and check some things based on this as I think I might have been going down the wrong path with SphericalTensorOperatorBasis in that case.

I will post back with notable successes or failures!

Cheers,
Johannes