Quantum mechanics in terms of ensemble in phase space

In the first part of this book, an alternative formalism of quantum mechanics based on statistical ensemble in phase space has been described. This book shows how to obtain the fundamental quantum-mechanical equation independently of the other formulations, and how to get the idea for operators pertaining to dynamical quantities. Moreover, it explains the approximation to the Schrodinger equation. In particular, it is demonstrated that this formalism can easily give the relativistic wave equation. The second part concerns the problem of interpretation. the author elucidates the foundation of uncertainty principle and presents the generalized proof of the uncertainty relations by use of commutation relations. The author shows that there cannot exist the measurement problem implicated in Apparatus and Observer. The author shows that the previous interpretation on the correspondence principle is not consistent in several respects. it is shown that it is possible to deduce the fundamental equation of quantum mechanics from the probability density, thus withdrawing a main assumption of quantum mechanics about the relation between the wave function and the probability density.