Lower bounds for solutions of the Schroedinger equation

Thesis/Dissertation · Sat Jan 01 04:00:00 EST 1983

OSTI ID:5345321

Froese, R G

For a large class of generalized N-body Hamiltonians H = -..delta.. + V the large absolute value x behavior of solutions to the Schroedinger equation H psi = H psi is studied. If E lies below the essential spectrum of H, then it is proved that lim R/sup -1/ log (absolute value psi/sub R/) = -..cap alpha../sub 0/ R ..-->.. infinity where absolute value psi/sub R//sup 2/ is the integral of absolute value psi/sup 2/ over a sphere of radius R and ..cap alpha../sub 0//sup 2/ + E is a threshold or ..cap alpha../sub 0/ 0. For E not necessarily below the essential spectrum of H, the same equation holds with absolute value psi/sub R//sup 2/ replaced by an integral of absolute value psi/sup 2/ over a spherical shell.

• Research Organization: Virginia Univ., Charlottesville (USA)
• OSTI ID: 5345321
• Country of Publication: United States
• Language: English

Related Subjects

657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANALYTICAL SOLUTION
DIFFERENTIAL EQUATIONS
EQUATIONS
HAMILTONIANS
MATHEMATICAL OPERATORS
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM OPERATORS
SCHROEDINGER EQUATION
WAVE EQUATIONS