Stern-Gerlach measurements with arbitrary spin: Quantum combs

摘要

As in quantum mechanics the operators of different Cartesian components of the angular momentum do not commute these observables cannot simultaneously have sharp values. In this paper we present a simple method to calculate the probability distributions for the measurements of angular momentum components other than (j) over cap(z) in eigenstates of (j) over cap(z) with an arbitrary value of j, where (h) over bar(2) j(j + 1) is the eigenvalue of (j) over cap(2). Surprisingly this method is not found in textbooks, where usually the case j = 1/2 is presented in discussions of Stern-Gerlach experiments. For larger values of j, the probability distributions have a comb-like structure. A detailed discussion of the quasiclassical limit j much greater than 1 is presented for the measurement of (j) over cap(x). It yields rather surprising results. (C) 2000 American Association of Physics Teachers. [References: 5]