Under the condition that the size of a device structure is comparable to the De Broglie wavelength of the electron, the transport properties of the device are described by the laws of quantum mechanics. The quantum ballistic regime is valid if the dimension of the structure is reduced below the mean free path of the electron [37]. The basic equations of quantum ballistic device simulations, namely the Poisson equation and the Schrödinger equation, are discussed in this section. Furthermore, we give attention to issues regarding boundary value problems that arise in semiconductor transport theory.