ISSN:
1572-9265
Schlagwort(e):
Moment problem
;
Schrödinger equation
;
inequalities
;
convexity
;
linear programming
Quelle:
Springer Online Journal Archives 1860-2000
Thema:
Informatik
,
Mathematik
Notizen:
Abstract We show that it is possible to project out in an exact manner the lowest eigenstate of Schrödinger equations. Taking into account the nodeless property of the lowest eigenstate one can replace the full Schrödinger equation by a moment problem whose measure is the eigenstate itself. The infinite set of positivity inequalities linked to this moment problem provides a framework which allows to compute sequences of upper and lower bounds to the unknown eigenvalue and eigenfunction. The effective computation is based on deep convexity properties embedded in the set of hierarchical inequalities associated to this moment problem. The convexity allows to get the bounds through linear programming. We illustrate the method with simple one dimensional problems.
Materialart:
Digitale Medien
URL:
http://dx.doi.org/10.1007/BF02141911
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