I have a problem understanding a point in the book "particle physics"
by B.R.Martin and G.shaw. The question is as following. A pair of
pion_plus-pion_minus is supposed to be in a state of definite orbital
angular momentum L . Now we apply charge conjugation operator on this
state which exchanges the two particles. According the book, the
resultant state vector is just (-1)^L times the original state vector,
"BECAUSE interchanging the pion_plus and pion_minus reverses their
relative position vector in the spatial wavefuction". I just can not
understand this "BECAUSE"! Could some one show me the detail of the
deduction. Thank you so much!

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I have a problem understanding a point in the book "particle physics"
by B.R.Martin and G.shaw. The question is as following. A pair of
pion_plus-pion_minus is supposed to be in a state of definite orbital
angular momentum L . Now we apply charge conjugation operator on this
state which exchanges the two particles. According the book, the
resultant state vector is just (-1)^L times the original state vector,
"BECAUSE interchanging the pion_plus and pion_minus reverses their
relative position vector in the spatial wavefuction". I just can not
understand this "BECAUSE"! Could some one show me the detail of the
deduction. Thank you so much!

The wave function for odd L is anti-symmetric:

psi( x ) = - psi( - x )

psi( x1, x2 ) = - psi( x2, x1 )

[Old Man]