The Equivalence Postulate of Quantum Mechanics

The Equivalence Principle (EP), stating that all physical systems are connected by a coordinate transformation to the free one with vanishing energy, univocally leads to the Quantum Stationary HJ Equation (QSHJE). Trajectories depend on the Planck length through hidden variables which arise as initial conditions. The formulation has manifest p-q duality, a consequence of the involutive nature of the Legendre transform and of its recently observed relation with second-order linear differential equations. This reflects in an intrinsic psi^D-psi duality between linearly independent solutions of the Schroedinger equation. Unlike Bohm's theory, there is a non-trivial action even for bound states. No use of any axiomatic interpretation of the wave-function is made. Tunnelling is a direct consequence of the quantum potential which differs from the usual one and plays the role of particle's self-energy. The QSHJE is defined only if the ratio psi^D/psi is a local self-homeomorphism of the extended real line. This is an important feature as the L^2 condition, which in the usual formulation is a consequence of the axiomatic interpretation of the wave-function, directly follows as a basic theorem which only uses the geometrical gluing conditions of psi^D/psi at q=\pm\infty as implied by the EP. As a result, the EP itself implies a dynamical equation that does not require any further assumption and reproduces both tunnelling and energy quantization. Several features of the formulation show how the Copenhagen interpretation hides the underlying nature of QM. Finally, the non-stationary higher dimensional quantum HJ equation and the relativistic extension are derived.Comment: 1+3+140 pages, LaTeX. Invariance of the wave-function under the action of SL(2,R) subgroups acting on the reduced action explicitly reveals that the wave-function describes only equivalence classes of Planck length deterministic physics. New derivation of the Schwarzian derivative from the cocycle condition. "Legendre brackets" introduced to further make "Legendre duality" manifest. Introduction now contains examples and provides a short pedagogical review. Clarifications, conclusions, ackn. and references adde

From a Mechanical Lagrangian to the Schr\"odinger Equation. A Modified Version of the Quantum Newton's Law

In the one-dimensional stationary case, we construct a mechanical Lagrangian describing the quantum motion of a non-relativistic spinless system. This Lagrangian is written as a difference between a function $T$, which represents the quantum generalization of the kinetic energy and which depends on the coordinate $x$ and the temporal derivatives of $x$ up the third order, and the classical potential $V(x)$. The Hamiltonian is then constructed and the corresponding canonical equations are deduced. The function $T$ is first assumed arbitrary. The development of $T$ in a power series together with the dimensional analysis allow us to fix univocally the series coefficients by requiring that the well-known quantum stationary Hamilton-Jacobi equation be reproduced. As a consequence of this approach, we formulate the law of the quantum motion representing a new version of the quantum Newton's law. We also analytically establish the famous Bohm's relation % $\mu \dot{x} = \partial S_0 /\partial x$ % outside of the framework of the hydrodynamical approach and show that the well-known quantum potential, although it is a part of the kinetic term, it plays really a role of an additional potential as assumed by Bohm.Comment: 20 pages, LateX, no figure, some calculations are reported in appendice

Cases on the Law of Partnership

Note to First Edition [1896]: The following collection of cases has been made primarily for use in connection with the writer\u27s lectures on Partnership in the Law School of this University and to accompany his \u27Elements of Partnership\u27 recently published. Note to Third Edition: In this edition the number of cases has again [from Second Edition] been considerably increased. F.R.M. ... October 1, 1905https://repository.law.umich.edu/books/1095/thumbnail.jp

Note on Comparability of MicroCog Test Forms

This study investigated the differences between the Standard and Short forms of MicroCog by comparing Domain scores for a clinical sample of 351 substance abusers which gave a significant difference between scores on the Spatial Processing Domain. Implications for research and clinical use are discussed

Advanced tracking systems design and analysis

The results of an assessment of several types of high-accuracy tracking systems proposed to track the spacecraft in the National Aeronautics and Space Administration (NASA) Advanced Tracking and Data Relay Satellite System (ATDRSS) are summarized. Tracking systems based on the use of interferometry and ranging are investigated. For each system, the top-level system design and operations concept are provided. A comparative system assessment is presented in terms of orbit determination performance, ATDRSS impacts, life-cycle cost, and technological risk

The heat kernel on the two-sphere

AbstractAn explicit full solution to the heat equation on the two-sphere is given

Presumptive identification of Candida species other than C. albicans, C. krusei, and C. tropicalis with the chromogenic medium CHROMagar Candida

BACKGROUND: CHROMagar Candida (CaC) is increasingly being reported as a medium used to differentiate Candida albicans from non-albicans Candida (NAC) species. Rapid identification of NAC can assist the clinician in selecting appropriate antifungal therapy. CaC is a differential chromogenic medium designed to identify C. albicans, C. krusei, and C. tropicalis based on colony color and morphology. Some reports have proposed that CaC can also reliably identify C. dubliniensis and C. glabrata. METHODS: We evaluated the usefulness of CaC in the identification of C. dubliniensis, C. famata, C. firmetaria, C. glabrata, C. guilliermondii, C. inconspicua, C. kefyr, C. lipolytica, C. lusitaniae, C. norvegensis, C. parapsilosis, and C. rugosa. RESULTS: Most NAC produced colonies that were shades of pink, lavender, or ivory. Several isolates of C. firmetaria and all C. inconspicua produced colonies difficult to differentiate from C. krusei. Most C. rugosa isolates produced unique colonies with morphology like C. krusei except in a light blue-green color. C. glabrata isolates produced small dark violet colonies that could be differentiated from the pink and lavender colors produced by other species. All seventeen isolates of C. dubliniensis produced green colonies similar to those produced by C. albicans. CONCLUSION: C. glabrata and C. rugosa appear distinguishable from other species using CaC. Some NAC, including C. firmetaria and C. inconspicua, could be confused with C. krusei using this medium