# Effective Hamiltonians and Quantum States

Lawrence C. Evans^{[1]}

- [1] Department of Mathematics, University of California, Berkeley

Séminaire Équations aux dérivées partielles (2000-2001)

- Volume: 2000-2001, page 1-13

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topEvans, Lawrence C.. "Effective Hamiltonians and Quantum States." Séminaire Équations aux dérivées partielles 2000-2001 (2000-2001): 1-13. <http://eudml.org/doc/11019>.

@article{Evans2000-2001,

abstract = {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 $\sigma $ solving a related transport equation.We present some elementary formal identities relating certain quantum states $\psi $ and $u, \sigma $. We show also how to build out of $u, \sigma $ an approximate solution of the stationary Schrödinger eigenvalue problem, although the error estimates for this construction are not very good.},

affiliation = {Department of Mathematics, University of California, Berkeley},

author = {Evans, Lawrence C.},

journal = {Séminaire Équations aux dérivées partielles},

language = {eng},

pages = {1-13},

publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},

title = {Effective Hamiltonians and Quantum States},

url = {http://eudml.org/doc/11019},

volume = {2000-2001},

year = {2000-2001},

}

TY - JOUR

AU - Evans, Lawrence C.

TI - Effective Hamiltonians and Quantum States

JO - Séminaire Équations aux dérivées partielles

PY - 2000-2001

PB - Centre de mathématiques Laurent Schwartz, École polytechnique

VL - 2000-2001

SP - 1

EP - 13

AB - 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 $\sigma $ solving a related transport equation.We present some elementary formal identities relating certain quantum states $\psi $ and $u, \sigma $. We show also how to build out of $u, \sigma $ an approximate solution of the stationary Schrödinger eigenvalue problem, although the error estimates for this construction are not very good.

LA - eng

UR - http://eudml.org/doc/11019

ER -

## References

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