  We study spontaneous symmetry breaking in one dimensional quantum mechanical
problems in terms of two-point boundary problems which lead to singular
potentials containing Dirac delta functions and its derivatives. We search for
broken-symmetry bound states. For a particular entanglement of boundary
conditions, we show the existence of a ground state, giving rise to a
spontaneous symmetry breaking, stable under the phenomenon of decoherence
generated from external fluctuations. We discuss the model in the context of
the "chiral" broken-symmetry states of molecules like $NH_3$.
