This is a collection of references (papers, books, preprints, book reviews, Ph. D. thesis, patents, web sites, etc.), sorted alphabetically and (some of them) classified by subject, on foundations of quantum mechanics and quantum information. Specifically, it covers hidden variables (``no-go'' theorems, experiments), interpretations of quantum mechanics, entanglement, quantum effects (quantum Zeno effect, quantum erasure, ``interaction-free'' measurements, quantum ``non-demolition'' measurements), quantum information (cryptography, cloning, dense coding, teleportation), and quantum computation.

/pdf/bibliographic-guide-to-the-foundations-of-quantum-mechanics-5bg1n4o4cz.pdf

Bibliographic guide to the foundations of quantum mechanics and quantum information

That space is not a void, that it is a separate entity, with defined structure, which has its own physical properties associated with it. While the search for the Graviton may continue, a much simpler and plausible alternative may be found in the study of a defined physical space.

https://www.rroij.com/open-access/theory-of-space-.pdf

Theory of Space

Atom-surface diffraction: A Trajectory description

The semiclassical method is characterized by finite forces and smooth, well-behaved trajectories, but also by multivalued representational functions that are ill behaved at caustics. In contrast, quantum trajectory methods—based on Bohmian mechanics (quantum hydrodynamics)—are characterized by divergent forces and erratic trajectories near nodes, but also well-behaved, single-valued representational functions. In this paper, we unify these two approaches into a single method that captures the best features of both, and in addition, satisfies the correspondence principle. Stationary eigenstates in one degree of freedom are the primary focus, but more general applications are also anticipated.

Reconciling semiclassical and Bohmian mechanics. I. Stationary states

Quantum dynamics of hydrogen atom in complex space

Quantum Newton's law

In the one-dimensional stationary case, we construct a mechanical Lagrangian describing the quantum motion of a nonrelativistic 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 to be 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 law We also analytically establish the famous Bohm relation outside the framework of the hydrodynamical approach and show that the well-known quantum potential, although it is a part of the kinetic term, plays really the role of an additional potential as assumed by Bohm

From a Mechanical Lagrangian to the Schrödinger Equation: A Modified Version of the Quantum Newton Law

Using the quantum Hamilton-Jacobi equation within the framework of the equivalence postulate, we construct a Lagrangian of a quantum system in one dimension and derive a third order equation of motion representing a first integral of the quantum Newton's law. We then integrate this equation in the free particle case and compare our results to those of Floydian trajectories. Finally, we propose a quantum version of Jacobi's theorem.

The Quantum Newton's Law

In this paper, we apply the one dimensional quantum law of motion, that we recently formulated in the context of the trajectory representation of quantum mechanics, to the constant potential, the linear potential and the harmonic oscillator. In the classically allowed regions, we show that to each classical trajectory there is a family of quantum trajectories which all pass through some points constituting nodes and belonging to the classical trajectory. We also discuss the generalization to any potential and give a new definition for de Broglie's wavelength in such a way as to link it with the length separating adjacent nodes. In particular, we show how quantum trajectories have as a limit when → 0 the classical ones. In the classically forbidden regions, the nodal structure of the trajectories is lost and the particle velocity rapidly diverges.

Trajectories in the Context of the Quantum Newton's Law

A unified form for real and complex wave functions is proposed for the stationary case, and the quantum Hamilton-Jacobi equation is derived in the three-dimensional space. The difficulties which appear in Bohm's theory like the vanishing value of the conjugate momentum in the real wave function case are surmounted. In one dimension, a new form of the general solution of the quantum Hamilton-Jacobi equation leading straightforwardly to the general form of the Schrodinger wave function is proposed. For unbound states, it is shown that the invariance of the reduced action under a dilatation plus a rotation of the wave function in the complex space implies that microstates do not appear. For bound states, it is shown that some freedom subsists and gives rise to the manifestation of microstates not detected by the Schrodinger wave function.

A. Bouda

Papers

Quantum Newton's law

From a Mechanical Lagrangian to the Schrödinger Equation: A Modified Version of the Quantum Newton Law

The Quantum Newton's Law

Trajectories in the Context of the Quantum Newton's Law

Probability Current and Trajectory Representation