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Effective Hamiltonians and Quantum States

Lawrence C. Evans

Séminaire Équations aux dérivées partielles

We recount here some preliminary attempts to devise quantum analogues of certain aspects of Mather’s theory of minimizing measures [M1-2, M-F], augmented by the PDE theory from Fathi [F1,2] and from [E-G1]. This earlier work provides us with a Lipschitz continuous function $u$ solving the eikonal equation aėȧnd a probability measure $σ$ solving a related transport equation. We present some elementary formal identities relating certain quantum states $ψ$ and $u, σ$ . We show also how to build out...

Estimates for smooth absolutely minimizing Lipschitz extensions.

Evans, Lawrence C. — 1993

Electronic Journal of Differential Equations (EJDE) [electronic only]

Page 1

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