### 1.1.1 Mathematical concepts and notations

The Hamiltonian operator in the Cartesian coordinate system is determined as

follows:

where **e**_{x}, **e** _{y}, **e**_{z} are the unit vectors of the Cartesian coordinate system. The operators grad, div, rot and ∆ are defined as follows:

Where *f*, **F** = (*F*_{x}, *F*_{y,} *F*_{z}) are the scalar and vector functions, (.,.) and [.,.] are the operations of the scalar and vector products, det *A* is the determinant of the matrix *A*.

The most important integral relationships of vector ...