do we have any application of vector(or cross) product of wave functions in quantum mechanics?
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.
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