Bethe Ansatz in Quantum Mechanics. 2. Construction of Multi-Parameter Spectral Equations

In this paper we propose a simple method for building exactly solvable multi-parameter spectral equations which in turn can be used for constructing completely integrable and exactly solvable quantum systems. The method is based on the use of a special functional relation which we call the scalar triangle equation because of its similarity to the classical Yang-Baxter equation.