The Relation Between Classical and Quantum Statistics

Klavs Hansen

Klavs Hansen

Walter Felipe Wreszinski, G. Scharf

Yong Huang

The classical statistical mean values are generally generalized to the quantum statistical mean values, the classical statistical uncertain relation is exactly generalized to quantum statistical uncertain relation, the two losed conditions in classical and quantum uncertain relations, respectively, are found, all articles and books relative to the two losed conditions need to be corrected. Finally, this paper generally expounds the relations among uncertain relation, singularity and the worlds stability, and gives the failure conditions of the quantum uncertain relation.

Y. C. HUANG, Ma, F C, N. ZHANG

Classical statistical average values are generally generalized to average values of quantum mechanics, it is discovered that quantum mechanics is direct generalization of classical statistical mechanics, and we generally deduce both a general new continuous eigenvalue equation and a general discrete eigenvalue equation in quantum mechanics, and discover that a eigenvalue of quantum mechanics is just an extreme value of an operator in possibility distribution, the eigenvalue f is just classical observable quantity. A general classical statistical uncertain relation is further given, the general classical statistical uncertain relation is generally generalized to quantum uncertainty principle, the two lost conditions in classical uncertain relation and quantum uncertainty principle, respectively, are found. We generally expound the relations among uncertainty principle, singularity and condensed matter stability, discover that quantum uncertainty principle prevents from the appearance of singularity of the electromagnetic potential between nucleus and electrons, and give the failure conditions of quantum uncertainty principle. Finally, we discover that the classical limit of quantum mechanics is classical statistical mechanics, the classical statistical mechanics may further be degenerated to classical mechanics, and we discover that only saying that the classical limit of quantum mechanics is classical mechanics is mistake. As application examples, we deduce both Shrodinger equation and state superposition principle, deduce that there exist decoherent factor from a general mathematical representation of state superposition principle, and the consistent difficulty between statistical interpretation of quantum mechanics and determinant property of classical mechanics is overcome.

K. Bruce Winterbon