In addition to the well-known case of spherical coordinates, the Schrödinger equation of the
hydrogen atom separates in three further coordinate systems. Separating in a particular …

The isotropic harmonic oscillator in dimension 3 separates in several different coordinate
systems. Separating in a particular coordinate system defines a system of three Poisson …

A Hamiltonian system is said to have nontrivial monodromy if its fundamental action-angle
loops do not return to their initial topological state at the end of a closed circuit in angular …

We show that spheroidal wave functions viewed as the essential part of the joint
eigenfunctions of two commuting operators on have a defect in the joint spectrum that makes …

Almost everything that happens in classical mechanics also shows up in quantum
mechanics when we know where to look for it. A phenomenon in classical mechanics …

In this thesis, we study three families of quantum integrable systems and the corresponding
special functions that arise from separation of variables. By analysing the respective …

An integrable Hamiltonian system presents monodromy if the action-angle variables cannot
be defined globally. As a prototype of classical monodromy with azimuthal symmetry, we …

A system is said to have monodromy if, when we carry the system around a closed circuit, it
does not return to its initial state. The simplest example is the square-root function in the …

In classical mechanics, one of the advanced topics is the study of action and angle
variables. These variables are quite abstract, but very powerful tools for describing classical …

The isotropic harmonic oscillator in dimension 3 separates in several different coordinate
systems. Separating in a particular coordinate system defines a system of three commuting …