  Justification of tight-binding model from Schroedinger formalism for various
topologies of position-based semiconductor qubits is presented in this work.
Simplistic tight-binding model allows for description of single-electron
devices at large integration scale. However it is due to the fact that
tight-binding model omits the integro-differential equations that arise from
electron-electron interaction in Schroedinger model. Two approaches are given
in derivation of tight-binding model from Schroedinger equation. First approach
is conducted by usage of Green functions obtained from Schroedinger equation.
Second approach is given by usage of Taylor expansion applied to Schroedinger
equation. The obtained results can be extended for the case of many Wannier
qubits with more than one electron and can be applied to 2 and 3 dimensional
model. Furthermore various correlation functions are proposed in Schroedinger
formalism that can account for static and time-dependent electric and magnetic
field polarizing given Wannier qubit system. One of the central results of
presented work relies on the emergence of dissipation processes during smooth
bending of semiconductor nanowires both in the case of classical and quantum
picture. Presented results give the base for physical description of
electrostatic Q-Swap gate of any topology using open loop nanowires. We observe
strong localization of wavepacket due to nanowire bending.
