On Quantum Operators as Statistical Random Variables Defined on a Spinning Roulette

A quantum operator is a classical physical variable except that it assumes values in a probability distribution, i.e., a random variable, solved by the Schrödinger equation in the form of a wavefunction. To date, the logical foundation of this construct remains an open question. This paper casts the basic components of quantum mechanics in the framework of general statistics. Our starting point is to define the domain of the wavefunction to be the complex unit circle, thus faithfully observing the periodicity of a wave. We seek to crystallize the meanings of the fundamental elements of quantum mechanics, which often are lost in its formalism, by certain common random variables in ordinary applications, such as random walks, inventory cycles, and human healthy temperatures, all defined on the sample space of a unit circle.