Let H =&( 2 Â2) 2+V(x) be a Schro dinger operator on R n , with smooth potential V(x) Ä + as |x| Ä + . The spectrum of H is discrete, and one can study the asymptotic of the smoothed spectral density We shall investigate the case where E is a critical value of the symbol H of H and, extending the w
✦ LIBER ✦
A semi-classical trace formula for Schrödinger operators
✍ Scribed by R. Brummelhuis; A. Uribe
- Publisher
- Springer
- Year
- 1991
- Tongue
- English
- Weight
- 978 KB
- Volume
- 136
- Category
- Article
- ISSN
- 0010-3616
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We prove multidimensional analogs of the trace formula obtained previously for one-dimensional Schro dinger operators. For example, let V be a continuous function on [0, 1] & /R & . For A/[1, ..., &], let &2 A be the Laplace operator on [0, 1] & with mixed Dirichlet Neumann boundary conditions .(x)=
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In this paper one obtains a result concerning the asymptotic behaviour of the spectral function on the diagonal for SCHRODINOER operators Ah = --A + V as h -+ 0. This asymptotic change the form on the energy level V ( x ) = A.