Author Topic: Cartesian interaction matrix into spherical tensor  (Read 4137 times)

johannes.mckay

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Cartesian interaction matrix into spherical tensor
« 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

JyrkiRantaharju

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Re: Cartesian interaction matrix into spherical tensor
« Reply #1 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.

johannes.mckay

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Re: Cartesian interaction matrix into spherical tensor
« Reply #2 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

MalcolmHLevitt

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Re: Cartesian interaction matrix into spherical tensor
« Reply #3 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.

johannes.mckay

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Re: Cartesian interaction matrix into spherical tensor
« Reply #4 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