Principles of Quantization

Heimo G. Latal, W. Schweiger

Andrei Yu. Khrennikov, Sergei Vladimirovich Kozyrev

The contextual probabilistic quantization procedure is formulated. This approach to quantization has much broader field of applications, compared with the canonical quantization. The contextual probabilistic quantization procedure is based on the notions of probability context and the principle of complementarity of probabilities. The general definition of probability context is given. The principle of complementarity of probabilities, which combines the ideas of the Bohr complementarity principle and the technique of noncommutative probability, is introduced. The principle of complementarity of probabilities is the criterion of possibility of the contextual quantization.

Gerald V. Dunne

Wang Wen-ze

The quantization energy and the quantization electron orbits of hydrogen atom and Bohr's quantization condition of the steady orbits (or the quantization condition of angular momentum) are educed with the correspondence principle.

John R. Klauder

Nik. A. Tyurin

This paper proposes a new way to quantize classical mechanical systems. Here we use ALAG - programme to construct moduli space of half weighted Bohr - Sommerfeld lagrangian cycles of fixed volume which is our quantum phase space. "Dynamical correspondence" principle makes possible to prove that this ALAG - quantization satisfies the Dirac correspondence principle. This construction relates two known quantizations using complex and real polarizations respectively.