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In case that two indential particals can be written as

Phi_1(r,t)=a_1|alpha>+b_1|beta>;
Phi_2(r,t)=a_2|alpha>+b_2|beta>;

then S==a_1^\ast a_2+b_1^\ast b_2;

If
Phi_1=exp(-i(\omega t - k r))|alpha>
Phi_2=exp(-i(\omega t - k r))|beta>;

|alpha>, |beta> are degenerate wavefunctions,

S is independent on the time, it is always equal to ZERO.

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