Question
Write down the wave function for . Use the isospin raising operator to derive the wavefunctions for
and
.
Answer :
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The pion triplet forms an isospin (I = 1) multiplet with third component (I_3 = +1, 0, -1). We start with the wavefunction of (\pi^-), which has (I_3 = -1). In terms of isospin states (|I, I_3\rangle): [ |\pi^-\rangle = |1, -1\rangle ] The isospin raising operator (I_+) acts as: [ I_+ |I, I_3\rangle = \sqrt{(I - I_3)(I + I_3 + 1)} , |I, I_3 + 1\rangle ] Apply (I_+) to (|\pi^-\rangle): [ I_+ |\pi^-\rangle = I_+ |1,
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