Stable quantum mechanical systems related to solutions of a triangle scalar equation

Stable (one-dimensional and multi-dimensional) accurately solvable (AS) and quasi-accurately solvable (QAS) quantum mechanical models are classified. Requirements for hamiltonian hermittivity and model stability cause definite restrictions on spectral parameters. The whole variety of AS an QAS models results from B(λ) function degeneration. The Schroedinger equations for these models are given. It is shown that trigonometrical, hyperbolic and elliptical QAS models exist only in curved spaces and can be classified using the given diagrams