Time decay and spectral kernel asymptotics

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

DOI:https://doi.org/10.1063/1.526563· OSTI ID:5990950

Osborn, T A; Wong, R

For quantum systems in R/sup 3/ defined by a Hamiltonian H given as the sum of the negative Laplacian perturbed by a real-valued potential v(x), the large time behavior of the fundamental solution of the time-dependent Schroedinger equation is investigated. For a suitably restricted class of potentials that have algebraic decay as Vertical BarxVertical Bar..-->..infinity, the continuous spectrum portion of the fundamental solution is characterized by an asymptotic expansion as t..-->.. +- infinity, which is uniform in compact subsets of R/sup 3/ x R/sup 3/. These results are then applied to derive the large energy asymptotic expansions of the spectral kernel associated with H.

• Research Organization: Department of Physics and Astronomy, University of Maryland, College Park, Maryland 20742
• OSTI ID: 5990950
• 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

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71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANALYTICAL SOLUTION
ASYMPTOTIC SOLUTIONS
BANACH SPACE
BOUNDARY CONDITIONS
DIFFERENTIAL EQUATIONS
EIGENFUNCTIONS
EQUATIONS
FOURIER TRANSFORMATION
FUNCTIONS
HAMILTONIANS
HILBERT SPACE
INTEGRAL TRANSFORMATIONS
KERNELS
LAPLACE TRANSFORMATION
LAPLACIAN
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
PARTIAL DIFFERENTIAL EQUATIONS
PERTURBATION THEORY
POTENTIALS
QUANTUM OPERATORS
REFLECTION
SCATTERING
SCHROEDINGER EQUATION
SERIES EXPANSION
SPACE
TIME DEPENDENCE
TRANSFORMATIONS
WAVE EQUATIONS