TY  - JOUR
A1  - Ludewig, Matthias
A1  - Rosenberger, Elke
T1  - Asymptotic eigenfunctions for Schrödinger operators on a vector bundle
JF  - Reviews in mathematical physics
N2  - In the limit (h) over bar -> 0, we analyze a class of Schrödinger operators H-(h) over bar = (h) over bar L-2 + (h) over barW + V .id(epsilon) acting on sections of a vector bundle epsilon over a Riemannian manifold M where L is a Laplace type operator, W is an endomorphism field and the potential energy V has a non-degenerate minimum at some point p is an element of M. We construct quasimodes of WKB-type near p for eigenfunctions associated with the low-lying eigenvalues of H-(h) over bar. These are obtained from eigenfunctions of the associated harmonic oscillator H-p,H-(h) over bar at p, acting on smooth functions on the tangent space.
KW  - Semi-classical analysis
KW  - WKB approximation
KW  - Schrödinger operators
KW  - semi-classical limit
Y1  - 2020
U6  - https://doi.org/10.1142/S0129055X20500208
SN  - 0129-055X
SN  - 1793-6659
VL  - 32
IS  - 7
PB  - World Scientific
CY  - Singapore
ER  -