Extension of the Quantum Mechanical Principle of Superposition to Non-Identical States with Short Life Times

We apply the principle of superposition to two quantum mechanical states of which one has a short life time 1/Γ. They must be identical, but may have a small difference in energy-momentum comparable to Γ. This produces new effects resulting from the linear relationship that appears between the S-matrix element and the production cross section of the decay products of the short lived state. An optical theorem for diffraction dissociation processes is proposed. This mechanism also provides a measure of the non-orthogonality between unstable particles that are eigenstates of a non-Hermitian Hamiltonian. Talk presented on the Workshop on Resonances and Time Asymmetric Quantum Theory, Jaca (Spain), 30 May to 4 June 2001     

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