Exactly solved Schrödinger equations with time-dependent Hamiltonians

• URL: http://arxiv.org/abs/2607.08450v1
• Date: Thu, 09 Jul 2026 13:13:09 GMT
• Title: Exactly solved Schrödinger equations with time-dependent Hamiltonians
• Abstract summary: We present the analytical, exact, explicit, and assumption free formulas for evolution operators corresponding to four instances of time-dependent Hamiltonians relevant to quantum spin batteries.<n>We demonstrate how to recover and go beyond existing expansions and approximations directly from the exact solutions giving, for example, an explicit exact formula for Floquet Hamiltonians at all orders.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present the analytical, exact, explicit, and assumption free formulas for the evolution operators corresponding to four instances of time-dependent Hamiltonians relevant to quantum spin batteries including two stochastic cases. We demonstrate how to recover and go beyond existing expansions and approximations directly from the exact solutions giving, for example, an explicit exact formula for Floquet Hamiltonians at all orders. The exact solutions are obtained through a completely novel combination of three mathematical techniques, the $\star$-algebra, path-sums and Omega calculus, which we briefly overview. These are widely applicable to other non-autonomous differential systems.

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