The Phenomena of Quantum Mechanics

Charles E. Burkhardt, Jacob J. Leventhal

Yasuda, Masao

Currently, dynamics of a massive macroparticle is given by classical analytical mechanics (CM), while that of a massive micro one is given by quantum mechanics (QM). We propose a mechanics effective for both: We transform, under coordinate transformation, the covariant tensor of order two underlying the kinetic energy term of the Hamilton-Jacobi (H-J) eq. of CM, not with the action of the diffeomorphism group, but with an action of an extended diffeomorphism group. Then, the H-J eq., a first-order partial differential eq., is modified to a third-order one. The Euler-Lagrange eq. of CM, a second-order ordinary differential eq., related to the H-J eq. through action integral of the least action principle is accordingly modified to a fourth-order one. We thus obtain a mechanics which, because of the higher-order eqs., accommodates phenomena corresponding to quantum phenomena. Energy of a particle in a confining potential is quantized to the same values as those of QM. Particle distribution in an ensemble disagrees with that of QM, but agrees with experiments within experimental uncertainty. The mechanics therefore is a testable alternative to QM.

P. A. M. Dirac

James T. Cushing

The ubiquity of chaos in classical mechanics (CM), as opposed to the situation in standard quantum mechanics (QM), might be taken as speaking against QM being the fundamental theory of physical phenomena. Bohmian mechanics (BM), as a formulation of quantum theory, may clarify both the existence of chaos in the quantum domain and the nature of the classical limit. Two interesting possibilities are (i) that CM and classical chaos are included in and underwritten by quantum mechanics (BM) or (ii) that BM and CM simply possess a common region of (noninclusive) overlap. In the latter case, neither CM nor QM alone would be sufficient, even in principle, to account for all of the physical phenomena we encounter. In this talk I shall summarize and discuss the implications of some recent work on chaos and on the classical limit within the framework of BM.

D. Baye, M. Dufour, Benjamin Fuks E

Şaki̇r Erkoç

Classical mechanics (CM) is applied to a wide range of dynamical systems, including the EM field of interaction with matter. On the other hand, quantum mechanics (QM) is more suitable for the description of phenomena on the atomic scale.