Quantum Mechanical Probabilities on a General Spacetime-Surface. II ---Nontrivial Example of Non-Interfering Alternatives in Quantum Mechanics---
A theoretical attempt is made to find a nontrivial example of a set of non-interfering (decohering) alternatives which are not restrictecd to an instant of time and for which quantum mechanical probabilities can be defined. Confining ourselves to nonrelativistic quantum mechanics for a particle, we find an example of such a set. The set consists of two alternatives which formally correspond to two outcomes of a `Yes-No' experiment. `Yes' is the occurrence that a particle is found on a given domain on a simple hypersurface in Newtonian spacetime, and `No' is the complement to `Yes'. in this example, absence of interference between the two alternatives is a consequence of a special choice of the symmetry of an initial amplitude. It turns out that the probabilities are 1 for `No' and 0 for `Yes'.