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I have a question regarding the CP operator on pion systems.

1) CP [itex] \mid \pi^0 \rangle [/itex]

2) CP [itex] \mid \pi^+ \pi^- \rangle [/itex]

3) CP [itex] \mid \pi^0 \pi^0 \rangle [/itex]

I'd like to solve this in the above ket notation and apply the operators as is on the different parts of the represented wave function. My solution for 2) is:

CP [itex] \mid \pi^+ \pi^- \rangle [/itex]

[itex] = C \mid \pi^- \pi^+ \rangle [/itex] (switch pions physically in e.g. x-coordinate)

[itex] = \mid \pi^+ \pi^- \rangle [/itex] (invert charges)

Thus CP is +1 for [itex] \mid \pi^+ \pi^- \rangle [/itex]. This does not seem to work for 1). Note I have somehow lost the notion of [itex] (-)^l [/itex] that should be present somewhere :S

Any help is appreciated.

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# CP on pion (combinations)

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