  We handle all the self-adjoint extensions of the minimal Schroedinger
operator for the non-relativistic electron living in the one-dimensional
configuration space with a junction. We are interested in every boundary
condition corresponding to the individual self-adjoint extension. Thus, we
clarify all the types of those boundary conditions of the wave functions of the
non-relativistic electron. We find a tunnel-junction formula for the
non-relativistic electron passing through the junction. Using this
tunnel-junction formula, we propose a mathematical possibility of a
tunnel-junction device for qubit.
