Geometrically induced spectrum of the schrödinger operator

الملخص EN

New and recent results concerning the spectrum of the operator with a boundary condition on a given curve in the (x,y)-plane are presented.

The geometry of the curve influences the nature of the spectrum, and the situations discussed are (i) there is a spectral interval [-c 2/ 4, ∞), (ii) there are discrete eigenvalues in [-∞, -c 2 /4).

The aim is to present material which avoids some of the technicalities in the literature.