A method for weight multiplicity computation based on Berezin quantization.
Applications of Lie systems in quantum mechanics and control theory
Some simple examples from quantum physics and control theory are used to illustrate the application of the theory of Lie systems. We will show, in particular, that for certain physical models both of the corresponding classical and quantum problems can be treated in a similar way, may be up to the replacement of the Lie group involved by a central extension of it. The geometric techniques developed for dealing with Lie systems are also used in problems of control theory. Specifically, we will study...
Dynamical symmetries in supersymmetric matrix models.
Introduction to cochains of differential operators
Introduction to Grassmann manifolds and quantum computation.
Non-commutative mechanics in mathematical and in condensed matter physics.
Quasi-exactly solvable Schrödinger operators in three dimensions.
Semiclassical quantization of circular billiard in homogeneous magnetic field: Berry-Tabor approach.
The spaces of quantum states for some harmonic oscillator potentials on the punctured plane C∖{0}
We consider equivariant solutions of Schrödinger equations on C∖{0} with harmonic oscillator potentials. We determine the spaces of equivariant quantum states in three cases: for an isotropic and anisotropic harmonic oscillator potential centered at 0, and for a potential not centered at 0.
The time-dependent Born-Oppenheimer approximation
We explain why the conventional argument for deriving the time-dependent Born-Oppenheimer approximation is incomplete and review recent mathematical results, which clarify the situation and at the same time provide a systematic scheme for higher order corrections. We also present a new elementary derivation of the correct second-order time-dependent Born-Oppenheimer approximation and discuss as applications the dynamics near a conical intersection of potential surfaces and reactive scattering.