Abstract

There has been a lot of interest in generalizing orthodox quantum mechanics to include POV measures as observables, namely as unsharp obserrables. Such POV measures are related to symmetric operators. We have argued recently that only maximal symmetric operators should describe observables.1 This generalization to maximal symmetric operators has many physical applications. One application is in the area of quantization. We shall discuss a scheme, to he called quantization by parts,which can systematically deal with what may be called quantum circuits. As a specific application we shall present a novel derivation of the famous Josephson equation for the supercurrent through a Josephson junction in a superconducting circuit. An interesting effect emerges from our quantization scheme when applied to a superconducting Y-shape circuit configuration. We also propose an experimental test for this effect which is expected to shed light on some conceptual problems on the quantum nature of the condensate