TY - JOUR
T1 - Time decay and spectral kernel asymptotics
AU - Osborn, T. A.
AU - Wong, R.
PY - 1985
Y1 - 1985
N2 - For quantum systems in ℝ3 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 Schrödinger equation is investigated. For a suitably restricted class of potentials that have algebraic decay as |x|→∞, the continuous spectrum portion of the fundamental solution is characterized by an asymptotic expansion as t→ ± ∞, which is uniform in compact subsets of ℝ3 X ℝ3. These results are then applied to derive the large energy asymptotic expansions of the spectral kernel associated with H. © 1985 American Institute of Physics.
AB - For quantum systems in ℝ3 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 Schrödinger equation is investigated. For a suitably restricted class of potentials that have algebraic decay as |x|→∞, the continuous spectrum portion of the fundamental solution is characterized by an asymptotic expansion as t→ ± ∞, which is uniform in compact subsets of ℝ3 X ℝ3. These results are then applied to derive the large energy asymptotic expansions of the spectral kernel associated with H. © 1985 American Institute of Physics.
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U2 - 10.1063/1.526563
DO - 10.1063/1.526563
M3 - RGC 21 - Publication in refereed journal
VL - 26
SP - 753
EP - 768
JO - Journal of Mathematical Physics
JF - Journal of Mathematical Physics
SN - 0022-2488
IS - 4
ER -