Pointwise bounds on eigenfunctions and wave packets in $N$-body quantum systems. I
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- by Barry Simon PDF
- Proc. Amer. Math. Soc. 42 (1974), 395-401 Request permission
Abstract:
We provide a simple proof of (a modification of) Kato’s theorem on the Hölder continuity of wave packets in N-body quantum systems. Using this method of proof and recent results of O’Connor, we prove a pointwise bound \[ |\Psi (\zeta )| \leqq {D_\varepsilon }\exp [ - (1 - \varepsilon ){a_0}|x|]\] on discrete eigenfunctions of energy E. Here $\varepsilon > 0,a_0^2 = 2$ (mass of the system) $[{\text {dist}}(E,{\sigma _{{\text {ess}}}})]$ and $|x|$ is the radius of gyration.References
- Reinhart Ahlrichs, Asymptotic behaviour of atomic bound state wave functions, Chem. Phys. Lett. 15 (1972), 609–612. MR 363232, DOI 10.1016/0009-2614(72)80386-5
- Tosio Kato, On the eigenfunctions of many-particle systems in quantum mechanics, Comm. Pure Appl. Math. 10 (1957), 151–177. MR 88318, DOI 10.1002/cpa.3160100201 A. O’Connor, Thesis, Princeton University, Princeton, N.J., 1972.
- A. J. O’Connor, Exponential decay of bound state wave functions, Comm. Math. Phys. 32 (1973), 319–340. MR 336119
- Barry Simon, Quantum mechanics for Hamiltonians defined as quadratic forms, Princeton Series in Physics, Princeton University Press, Princeton, N. J., 1971. MR 0455975
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 42 (1974), 395-401
- MSC: Primary 35P99; Secondary 81.47
- DOI: https://doi.org/10.1090/S0002-9939-1974-0417596-0
- MathSciNet review: 0417596