By W.S.C. WILLIAMS (Eds.)
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Extra resources for An Introduction to Elementary Particles
Thus the parity of the eigenfunction 7(/, l ) is (— 1)'. In quantum-mechnical language the spherical harmonic 7(/, l ) is the amplitude for finding a particle at a particular angle if it is in the state that is the eigenstate of L and L with eigenvalues /, / . Suppose that this state is represented by the vector | /, / ) ; then we use the following notation: the amplitude for finding the particle at the polar angles 0, φ is <θ,φ\1,0= Υ,'φ,φ). 58) z z 2 z z z A useful value is <β = 0 , φ = 0 \ /, l } = [(21 + 1)/4ττ] if /, = 0, and 0 if l Φ 0.
We shall use the Wigner-Eckart theorem as a method of comparing transition rates in strange-particle decays. 13 Polarization Polarization is an important phenomenon in elementary-particle physics. Targets of polarized protons are available, and the decay of hyperons and baryon resonances gives information on their polarization. The polarization of proton or neutron beams may be analyzed by scattering. Thus the ability to measure or produce polarization gives us further means of examining elementary-particle interactions.
Under these circumstances the matrix refers to mixed spin states of a system of particles. The important properties of the density matrix are as follows. 58 II. Angular Momentum (1) The density matrix is Hermitian. This follows from the fact that (Q} is a real quantity and Q is a Hermitian operator; therefore Pirn — 9ml · (2) Since any particle of a system must be in one of the available states, we require Tr ρ = 1 . Later we shall be using two matrices p and p which represent the spin states of a beam of incident particles and a beam of scattered particles re spectively.
An Introduction to Elementary Particles by W.S.C. WILLIAMS (Eds.)