  It is now common practice to solve the Schr\"odinger equation to estimate the
tunneling current between two electrodes at specified potentials, or the
transmission through a potential barrier by assuming that there is an incident,
reflected, and transmitted wave. However, these two approaches may not be
appropriate for applications with nanoscale circuits. A new approach is
required because the electron man-free path may be as long as 68.2 nm in metals
so it is possible that the wavefunction may be coherent throughout a nanoscale
circuit. We define several algorithms for determining the eigenvalues with
different sets of the circuit parameters, thus demonstrating the existence of
consistent solutions for nanoscale circuits. We also present another algorithm
that is being applied to determine the full solution for nanoscale circuits.
All of this is done using only analytical solutions of the Schr\"odinger
equation.
