I did not understand the question, my remark might therefore be inappropriate.

To apply cross product like in ordinary vector algebra I should be able to construct a vector,starting from the wave function amplitude. This is possible using e.g. the transition amplitudes in two level systems. The procedure gives rise to a vector and the relevant Scoroedinger equation can be written in terms of a Bloch equation involving a vector cross product.

A more elaborated procedure occurs in relativistic quantum mechanics, when spin is involved.

If you can provide a specific example I might be more helpful.

The best

Pino

This procedure occurs in relativistic quantum mechanics, for some spin systems.