Electronic Resource
Springer
Communications in mathematical physics
75 (1980), S. 239-261
ISSN:
1432-0916
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Abstract Schrödinger operators with interactions symmetric about a plane (double-well potentials) occur in several branches of physics, such as chemistry and quantum field theory. They commonly exhibit asymptotic eigenvalue degeneracy, i.e., pairs of eigenvalues coalesce as the potential wells get farther apart. After a sketch of the theory of double wells, it is shown that the problem of estimating the gap between two such eigenvalues is reducible to finding asymptotics of eigenfunctions. For several examples and classes of potentials the gap is estimated or bounded above and below. The general case is fullyn-dimensional.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01212711
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