新量子論の基本原理

In this article, we established the fundamental principles of new quantum theory.
At first, we mention the notion of quantum probability and its basic properties.
Next, we propose the axiom of new quantum theory, using the notion of quantum probability. The characteristic property of the quantum state is that the quantum state is determined by the L2-density of the quantum probability distribution of the position variables and the momentum variables of the quantum system.
At last, we derive the Schrödinger equations by the reasonable method based on the axiom of new quantum theory. Here we use the variational principle that the real L2-density determining the quantum state of the quantum system, which is, in practice, realized physically, should be determined among the admissible L2-densities so that the energy expectation value takes its stationary value.