Parameter differentiation for time varying Schrodinger equations

Parameter differentiation and quantum state decomposition for time varying Schrodinger equations

Claudio Altafini

Reports on Mathematical Physics, 52(3):381-400, 2003 (also preprint arXiv:quant-ph/0201034).

For the unitary operator, solution of the Schrodinger equation corresponding to a time-varying Hamiltonian, the relation between the Magnus and the product of exponentials expansions can be expressed in terms of a system of first order differential equations in the parameters of the two expansions. A method is proposed to compute such differential equations explicitly and in a closed form.

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