  The theory of interaction at one point is developed for the one-dimensional
Schrodinger equation. In analog with the three-dimensional case, the resulting
interaction is referred to as the Fermi pseudo-potential. The dominant feature
of this one-dimensional problem comes from the fact that the real line becomes
disconnected when one point is removed. The general interaction at one point is
found to be the sum of three terms, the well-known delta-function potential and
two Fermi pseudo-potentials, one odd under space reflection and the other even.
The odd one gives the proper interpretation for the delta'(x) potential, while
the even one is unexpected and more interesting. Among the many applications of
these Fermi pseudo-potentials, the simplest one is described. It consists of a
superposition of the delta-function potential and the even pseudo-potential
applied to two-channel scattering. This simplest application leads to a model
of the quantum memory, an essential component of any quantum computer.
