Around spectral theory of Schrödinger equation with polynomial potential in C

by Boris Shapiro (Stockholm University, Math. Department)

Monday 4 Feb 2013, 13:30 → 14:30 Europe/Stockholm

122:026

Various spectral properties of Schödinger equations with polynomial potential in the complex plane C were studied by mathematicians since the early 1930's. In physics this class of problems attracted considerable attention since the break-trough publication of C.M.Bender and T.T.Wu in 1969 about surprising spectral properties of the quartic oscillator depending on a complex parameter. In this talk I will survey some old and very new results in this area and pose a number of open problems related to spectral asymptotics, asymptotic root distributions of eigenfunctions, and parameter values for which eigenvalues collide. No serious mathematical background will (hopefully) be necessary.