Consider a spin-1/2 particle passing through a series of spin filters, as in Fig XXXXXXXXXXNow, however, there are 13 filters (numbered 0 through 12). The nth filter selects for the state |n+, the +/2...

Consider a spin-1/2 particle passing through a series of spin filters, as in Fig. 2.13. Now, however, there are 13 filters (numbered 0 through 12). The nth filter selects for the state |n+, the +/2 basis state for a measurement of spin along an axis in the xz-plane an angle nπ/12 from z. From Eq. 2.35, we can write

What is the probability that a spin-1/2 particle, initially in the state |z+, will pass all 13 filters?