Introduction. – The non-relativistic system of a onedimensional infinite square well with a massive particle evolving according to the Schrödinger equation is one of the most elementary quantum mechanical systems, and it often serves as an approximation to more complex physical systems. If, however, the potential walls are allowed to move, as originally in the Fermi-Ulam model for the accelerat...

From the partial differential Calogero’s (three-body) and Smorodinsky-Winternitz (superintegrable) Hamiltonians in two variables we separate the respective angular Schrödinger equations and study the possibilities of their “minimal” PT symmetric complexification. The simultaneous loss of the Hermiticity and solvability of the respective angular potentials V (φ) is compensated by their replaceme...

We consider a non relativistic charged particle in a 1D infinite square potential well. This quantum system is subjected to a control, which is a uniform (in space) time depending electric field. It is represented by a complex probability amplitude solution of a Schrödinger equation on a 1D bounded domain, with Dirichlet boundary conditions. We prove the almost global approximate stabilization ...

Given a non-hermitean matrix M, the structure of its minimal polynomial encodes whether M is diagonalizable or not. This note will explain how to determine the minimal polynomial of a matrix without going through its characteristic polynomial. The approach is applied to a quantum mechanical particle moving in a square well under the influence of a piece-wise constant PT-symmetric potential. Upo...

Continuing our investigation into the numerical properties of the hierarchical reference theory, we study the square well fluid of range l from slightly above unity up to 3.6. After briefly touching upon the core condition and the related decoupling assumption necessary for numerical calculations, we shed some light on the way an inappropriate choice of the boundary condition imposed at high de...

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