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In most introductory courses on quantum mechanics one is taught that the Hamiltonian operator must be Hermitian in order that the energy levels be real and that the theory be unitary (probability conserving). To express the Hermiticity of a…

Quantum Physics · Physics 2008-11-26 Carl M. Bender

A hybrid formalism is proposed for interacting classical and quantum sytems. This formalism is mathematically consistent and reduces to standard classical and quantum mechanics in the case of no interaction. However, in the presence of…

Quantum Physics · Physics 2009-11-06 Asher Peres , Daniel Terno

We discuss the notion about physical quantities as having values represented by real numbers, and its limiting to describe nature to be understood in relation to our appreciation that the quantum theory is a better theory of natural…

Quantum Physics · Physics 2021-01-13 Otto C. W. Kong , Wei-Yin Liu

Some notes about quantum physics, an interpretation if one wishes, are put forward, insisting on `closely following the mathematics/formalism, the `nuts and bolts of what quantum physics says'. These, basically well-known, issues seem to…

Quantum Physics · Physics 2022-01-03 Eliahu Levy

In this paper, we investigate the connection between Classical and Quantum Mechanics by dividing Quantum Theory in two parts: - General Quantum Axiomatics (a system is described by a state in a Hilbert space, observables are self-adjoint…

Quantum Physics · Physics 2009-11-07 H. Bergeron

Quantum Darwinism is a paradigm to understand how classically objective reality emerges from within a fundamentally quantum universe. Despite the growing attention that this field of research as been enjoying, it is currently not known what…

Quantum Physics · Physics 2025-10-15 Emery Doucet , Sebastian Deffner

Bohmian mechanics is a realistic interpretation of quantum theory. It shares the same ontology of classical mechanics: particles following continuous trajectories in space through time. For this ontological continuity, it seems to be a good…

Quantum Physics · Physics 2016-03-11 Davide Romano

A recent notion in theoretical physics is that not all quantum theories arise from quantising a classical system. Also, a given quantum model may possess more than just one classical limit. These facts find strong evidence in string duality…

High Energy Physics - Theory · Physics 2008-11-26 J. M. Isidro

In recent decades, an important shift has taken place with the growing role of non-Hermitian quantum mechanics. What makes this framework remarkable is that the eigenvalues of the Hamiltonians involved can still be real, just as in the…

Quantum Physics · Physics 2025-09-30 Maamache Mustapha

Relativistic quantum mechanics can be considered to have begun with a search for wave equations corresponding to each intrinsic spin. However, relativistic quantum physics differs fundamentally from the non-relativistic wave mechanics. It…

History and Philosophy of Physics · Physics 2026-03-09 Urjit A. Yajnik

We generalize the Hamiltonian picture of General Relativity coupled to classical matter, known as geometrodynamics, to the case where such matter is described by a Quantum Field Theory in Curved Spacetime, but gravity is still described by…

General Relativity and Quantum Cosmology · Physics 2024-03-20 J. L. Alonso , C. Bouthelier-Madre , J. Clemente-Gallardo , D. Martínez-Crespo

It is generally accepted that quantum mechanics entails a revision of the classical propositional calculus as a consequence of its physical content. However, the universal claim according to which a new quantum logic is indispensable in…

History and Philosophy of Physics · Physics 2020-12-04 Andrea Oldofredi

In this paper a quantum mechanics is built by means of a non-Hermitian momentum operator. We have shown that it is possible to construct two Hermitian and two non-Hermitian type of Hamiltonians using this momentum operator. We can construct…

Mathematical Physics · Physics 2011-03-25 Juan M. Romero , O. Gonzalez-Gaxiola , J. Ruiz de Chavez , R. Bernal-Jaquez

In this paper we discuss the relevance of the algebraic approach to quantum phenomena first introduced by von Neumann before he confessed to Birkoff that he no longer believed in Hilbert space. This approach is more general and allows us to…

Quantum Physics · Physics 2014-08-26 Basil J. Hiley

I argue that quantum mechanics is fundamentally a theory about the representation and manipulation of information, not a theory about the mechanics of nonclassical waves or particles. The notion of quantum information is to be understood as…

Quantum Physics · Physics 2009-11-10 Jeffrey Bub

This paper is a programmatic article presenting an outline of a new view of the foundations of quantum mechanics and quantum field theory. In short, the proposed foundations are given by the following statements: * Coherent quantum physics…

Quantum Physics · Physics 2019-05-21 Arnold Neumaier

After the development of a self-consistent quantum formalism nearly a century ago, there ensued a quest to understand the often counterintuitive predictions of the theory. These endeavors invariably begin with the assumption of the "truth"…

History and Philosophy of Physics · Physics 2019-10-22 Stephen Boughn

A recent concept in theoretical physics, motivated in string duality and M-theory, is the notion that not all quantum theories arise from quantising a classical system. Also, a given quantum model may possess more than just one classical…

Quantum Physics · Physics 2007-05-23 J. M. Isidro

Classical and quantum physics represent two distinct theories; however, quantum physics is regarded as the more fundamental of the two. It is posited that classical mechanics should arise from quantum mechanics under certain limiting…

Quantum Physics · Physics 2026-01-21 Abdul Rahaman Shaikh , Tabish Qureshi

Fuchs and Peres (2000) claimed that standard Quantum Mechanics needs no interpretation. In this essay, I show the flaws of the arguments presented in support to this thesis. Specifically, it will be claimed that the authors conflate QM with…

Quantum Physics · Physics 2019-04-26 Andrea Oldofredi
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