Perturbation of Schroedinger Hamiltonians by measures: Self-adjointness and lower semiboundedness

Journal Article · Mon Apr 01 04:00:00 EST 1985 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.526598· OSTI ID:5968178

Brasche, J

We study the Hamiltonians for nonrelativistic quantum mechanics in one dimension, in terms of energy forms ..integral..Vertical Bardf/dxVertical Bar/sup 2/ dx+..integral..Vertical Bar f Vertical Bar/sup 2/ d( ..mu.. -..nu..), where ..mu.. and ..nu.. are positive, not necessarily finite measures on the real line. We cover, besides regular potentials, cases of very singular interactions (e.g., a particle interacting with an infinite number of fixed particles by ''delta function potentials'' of arbitrary strengths). We give conditions for lower semiboundedness and closability of the above energy forms, which are sufficient and, for certain classes of potentials (e.g., ..mu..-..nu.. a signed measure), also necessary. In contrast to the results in other approaches, no regularity conditions and no restrictions on the growth of the measures ..mu.. and ..nu.. at infinity are needed.

• Research Organization: Fakultaet fuer Mathematik, Universitaet Bielefeld, Universitaetsstrasse 1, 4800 Bielefeld 1, Federal Republic of Germany
• OSTI ID: 5968178
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 26:4; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

645201* -- High Energy Physics-- Particle Interactions & Properties-Theoretical-- General & Scattering Theory
645400 -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ASYMPTOTIC SOLUTIONS
BANACH SPACE
BOUNDARY CONDITIONS
DELTA FUNCTION
DIFFERENTIAL EQUATIONS
DISTRIBUTION FUNCTIONS
DISTURBANCES
DYNAMICS
EQUATIONS
FUNCTIONAL ANALYSIS
FUNCTIONS
HAMILTONIANS
HILBERT SPACE
INTERACTIONS
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MATHEMATICS
MEASURE THEORY
MECHANICS
PARTICLE INTERACTIONS
PERTURBATION THEORY
POLARIZATION
POTENTIALS
QUANTUM MECHANICS
QUANTUM OPERATORS
SPACE
STABILITY