Notation

$x$	...	Scalar
$x^\ast$	...	Complex conjugate of $x$
${\mathbf{x}}$	...	Vector
$\ensuremath{{\underline{A}}}$	...	Matrix
$A_{ij}$	...	Elements of the matrix ${\underline{A}}$
$\ensuremath{{\underline{A}}}^+$	...	Conjugate transposed matrix: $A_{ij} = A_{ji}^\ast$
$\mathbf{e}_x$	...	Unity vector in direction x
$\mathbf{x} \cdot \mathbf{y}$	...	Scalar (in) product
$\partial_t(\cdot)$	...	Partial derivative with respect to $t$
$\ensuremath{{\mathbf{\nabla}}}$	...	Nabla operator
$\ensuremath{{\mathbf{\nabla}}}\mathbf{x}$	...	Gradient of ${\mathbf{x}}$
$\ensuremath{{\mathbf{\nabla}}}\cdot \mathbf{x}$	...	Divergence of ${\mathbf{x}}$
$\ensuremath{{\mathbf{\nabla}}}\cdot \ensuremath{{\mathbf{\nabla}}}= \ensuremath{{\mathbf{\nabla}}}^2$	...	LAPLACE operator
$\Gamma(\cdot)$	...	Gamma function
$\Gamma_i(\cdot,\cdot)$	...	Incomplete gamma function
$\langle\cdot\rangle$	...	Statistical average
$f(\mathbf{r},\mathbf{k},t)$	...	Distribution function
$\mathcal{Q}(f)$	...	Collision operator
$\ensuremath{{\underline{H}}}$	...	HAMILTONian operator
$\ensuremath{{\underline{G}}}$	...	GREEN's function
$\ensuremath{{\underline{I}}}$	...	Unity matrix
$\ensuremath{{\underline{T}}}$	...	Transfer matrix
$\ensuremath{\mathrm{det}}(\cdot)$	...	Determinant of a matrix
$\mathcal{F}_i$	...	FERMI integral of order $i$
$\ensuremath{\mathrm{Ai}}(\cdot)$, $\ensuremath{\mathrm{Bi}}(\cdot)$	...	AIRY functions
$\ensuremath{\mathrm{Ai'}}(\cdot)$, $\ensuremath{\mathrm{Bi'}}(\cdot)$	...	Derivative of the AIRY functions

A. Gehring: Simulation of Tunneling in Semiconductor Devices