This article reviews the role of hidden symmetries of dynamics in the study of physical
systems, from the basic concepts of symmetries in phase space to the forefront of current …

The nonlinear supersymmetric (SUSY) approach to spectral problems in quantum
mechanics (QM) is reviewed. Its building from the chains (ladders) of linear SUSY systems is …

We show that some simple well-studied quantum mechanical systems without fermion (spin)
degrees of freedom display, surprisingly, a hidden supersymmetry. The list includes the …

The origin of spectral singularities in finite-gap singly periodic PT-symmetric quantum
systems is investigated. We show that they emerge from a limit of band-edge states in a …

The ordering problem in quantum systems with position-dependent mass (PDM) is treated
by inclusion of the classically fictitious similarity transformation into the kinetic term. This …

We explain the origin and the nature of a special nonlinear supersymmetry of a
reflectionless Pöschl–Teller system by the Aharonov–Bohm effect for a non-relativistic …

A bstract We investigate a special class of the\(\mathcal {P}\mathcal {T}\)-symmetric quantum
models being perfectly invisible zero-gap systems with a unique bound state at the very …

We show that an n-gap periodic quantum system with parity-even smooth potential admits 2
n− 1 isospectral super-extensions. Each is described by a tri-supersymmetry that originates …

The hidden supersymmetry and related tri-supersymmetric structure of the free particle
system, the Dirac delta potential problem and the Aharonov–Bohm effect (planar, bound …

A bosonized nonlinear (polynomial) supersymmetry is revealed as a hidden symmetry of the
finite-gap Lamé equation. This gives a natural explanation for peculiar properties of the …