16-91 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 one-dimensional quantum particle in multiple potential wells separated by barriers. We show that, for each eigenvalue of the Schr\"odinger operator, the Bohr-Sommerfeld 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 Bohr-Sommerfeld condition.

Files: 16-91.src( 16-91.keywords , BARRIER.pdf.mm )