# Solution to the Schrodinger equation for periodically time dependent Hamiltonians

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I have a Hamiltonian which is time dependent but possesses periodic symmetry: $H(t+t_0)=H(t)$. Is there any clever techniques to exploit this? Edit: In particular, I would like a practical method to simulate the dynamics of such a system (as opposed to naive time-slicing).

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asked Jan 25, 2012
retagged Mar 7, 2014
Do you want dynamics or average ground state?

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@JoeFitzsimons -- good question. This was an example question I used at a StackExchange participation drive, so I unfortunately didn't give it much thought. I will make it clearer now.

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## 1 Answer

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I would suggest looking at the formalism of Floquet space. The basic idea is that one uses a time-independent but infinite dimensional Hamiltonian to simulate evolution under a time-dependent but finite dimensional Hamiltonian by using a new index to label terms in a Fourier series.

A good, short introduction can be found in Levante et al. For more details, Leskes et al provides a very through review. Finally, a simple example of an application of Floquet theory is given by Bain and Dumont.

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answered Jan 25, 2012 by (260 points)
Chris, can you add some comments about truncating the series in order to implement this method?

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