 1691 D. R. Yafaev
 Passage through a potential barrier and multiple wells
(464K, .pdf)
Nov 16, 16

Abstract ,
Paper (src),
View paper
(auto. generated pdf),
Index
of related papers

Abstract. Consider the semiclassical limit, as the Planck constant $\hbar
i 0$, of bound states of a onedimensional quantum particle in multiple potential wells separated by barriers. We show that, for each eigenvalue of the Schr\"odinger operator, the BohrSommerfeld quantization condition is satisfied at least for one potential well. The proof of this result relies on a study of real wave functions in a neighborhood of
a potential barrier. We show that, at least from one side, the barrier fixes the phase of wave functions in the same way as a potential barrier of infinite width. On the other hand, it turns out that for each well there exists an eigenvalue in a small neighborhood of every point satisfying the BohrSommerfeld condition.
 Files:
1691.src(
1691.keywords ,
BARRIER.pdf.mm )