Inverse spectral theory for semiclassical Jaynes–Cummings systems

Semiclassical Inverse Spectral Theory for Singularities of Focus-focus Type

We prove, assuming that the Bohr-Sommerfeld rules hold, that the joint spectrum near a focus-focus critical value of a quantum integrable system determines the classical Lagrangian foliation around the full focus-focus leaf. The result applies, for instance, to ~-pseudodifferential operators, and to Berezin-Toeplitz operators on prequantizable compact symplectic manifolds.

Inverse Spectral Theory for One

Symplectic inverse spectral theory for pseudodifferential operators

We prove, under some generic assumptions, that the semiclassical spectrum modulo O(~) of a one dimensional pseudodifferential operator completely determines the symplectic geometry of the underlying classical system. In particular, the spectrum determines the hamiltonian dynamics of the principal symbol.

Inverse spectral problems for Sturm-Liouville operators with transmission conditions

Abstract: This paper deals with the boundary value problem involving the differential equation                      -y''+q(x)y=lambda y                                 subject to the standard boundary conditions along with the following discontinuity conditions at a point              y(a+0)=a1y(a-0),    y'(a+0)=a2y'(a-0)+a3y(a-0).  We develop the Hochestadt-Lieberman’s result for Sturm-Lio...

New Approach to Inverse Spectral Theory