Top Research Papers on Quantum Mechanics

A discussion on the quantum mechanics of oneand many-particle systems on the quantum spheres is presented. The role of quantum group symmetry is fully exploited and developed. Generalized dynamical systems are introduced and discussed. We present the concept of generalized homogeneous spaces, and obtain the analogue of topological charges through inequivalent quantizations. The importance and origin of braiding in multi-particle systems is explained. r··· . --. '" -y • """, ".-*r ~·~-~·~ ...-t .... , f l ; j " :. . 1

A real-valued symplectic group underlies the dynamics of quantum-mechanical systems. Exploring the embedding of unitary groups clarifies the relation of non-Hermitian - and -symmetric quantum theories of recent interest. Symmetries of the full dynamical framework are quite rich and reveal new viewpoints on many topics in quantum theory. Transformations mixing ‘upper’ and ‘lower’ components of certain symplectic multiplets are indistinguishable from coupling antimatter degrees of freedom. Quantities long identified with physical observables are valid canonical coordinates of the theory, without...

These are the author's lectures at the 1992 Les Houches Summer School, "Gravitation and Quantizations". They develop a generalized sum-over-histories quantum mechanics for quantum cosmology that does not require either a preferred notion of time or a definition of measurement. The "post-Everett" quantum mechanics of closed systems is reviewed. Generalized quantum theories are defined by three elements (1) the set of fine-grained histories of the closed system which are its most refined possible description, (2) the allowed coarse grainings which are partitions of the fine-grained histories int...

What is quantum mechanics and what does it do? In very general terms, the basic problem that both classical Newtonian mechanics and quantum mechanics seek to address can be stated very simply: if the state of a dynamic system is known initially and something is done to it, how will the state of the system change with time in response? In this chapter, we will give a brief overview of, first, how Newtonian mechanics goes about solving the problem for systems in the macroscopic world and, then, how quantum mechanics does it for systems on the atomic and subatomic scale. We will see qualitatively...

Bohmian mechanics allows us to understand quantum systems in the light of other quantum traits than the well-known ones (coherence, diffraction, interference, tunnelling, discreteness, entanglement, etc.). Here the discussion focusses precisely on two of these interesting aspects, which arise when quantum mechanics is thought within this theoretical framework: the non-crossing property, which allows for distinguishability without erasing interference patterns, and the possibility to define quantum probability tubes, along which the probability remains constant all the way. Furthermore, taking ...

This article looks at the postulates of quantum mechanics, a mathematical theory currently being developed to give a theoretical basis for building a "quantum computer," which is claimed to be faster than any classical computer to date.

Based on a deformation of the quantum mechanical phase space we study q-deformations of quantum mechanics for qk=1 and 0<q<1. After defining a q-analog of the scalar product on the function space we discuss and compare the time evolution of operators in both cases. A formulation of quantum mechanics for qk=1 is given and the dynamics for the free Hamiltonian is studied. For 0<q<1 we develop a deformation of quantum mechanics and the cases of the free Hamiltonian and the one with a x2-potential are solved in terms of basic hypergeometric functions.

The paper attempts to explain how the result of quantum mechanics is the natural obstacle to the existing computer technology--10 10 m is the limit of the integration of the fuse slice.

In Quantum mechanics, quantum decoherence is the loss of coherence or ordering of the phase angles between the components of a system in a quantum superposition. One consequence of this dephasing is classical or probabilistically additive behavior. Quantum decoherence gives the appearance of wave function collapse (the reduction of the physical possibilities into a single possibility as seen by an observer) and justifies the framework and intuition of classical physics as an acceptable approximation: decoherence is the mechanism by which the classical limit emerges from a quantum starting poin...

The book provides the basic concepts of quantum mechanics including postulates, operators, basic of formalism, quantum computation, virtual environment and biological simulations etc.

Incompatibility between conjugate variables and complementary pictures comes in two kinds, exclusive of one another. The first kind is unconditional, and the second conditional on quantum's indivisibility. We employ this distinction to study the wave-particle dualism and the energy-time uncertainty relation. Afterwards we look upon the present state of the quantum mechanical formalism. We demonstrate that the two incompatibilities are employed in the same treatment forming a "hybrid" description of the phenomena and leading to a contradiction.

The following notes from lectures given at the mathematics department of George Washington University are meant to be a partial remedy to the situation, offering a very brief and slightly unorthodox introduction to one-particle quantum mechanics.

This thesis analyzes the epistemological implications and the role of basic concepts like information, physical law and matter in characterizing the physical reality. The key point will be a quantum description of this physical reality. Once fixed at ontic level two basic elements, namely the laws of physics and the matter, we argue that the underlying physical reality emerges from the interconnection between these two elements. We consider any physical process, including measurement, modeled by unitary evolution. In this context, we deduce quantum randomness as a consequence of inclusion o...

We show that the standard Heisenberg algebra of quantum mechanics admits a noncommutative differential calculus Ω1 depending on the Hamiltonian p2/2m + V(x), and a flat quantum connection ∇ with torsion such that a previous quantum-geometric formulation of flow along autoparallel curves (or “geodesics”) is exactly Schrödinger’s equation. The connection ∇ preserves a non-symmetric quantum metric given by the canonical symplectic structure lifted to a rank (0, 2) tensor on the extended phase space where we adjoin a time variable. We also apply the same approach to obtain a novel flow generated b...

Some thoughts of the quantum mechanics have produced great influence on people's philosophic ideas and the core thought of the quantum mechanics is “Wave-particle duality”, Bohr's Complementary principle,Uncertainty Principle and Causality relate to probability. Quantum mechanics has nothing to do with idealism and agnosticism, but it emphasizes logic substantial evidence, making researches into the microcosmic particles' behavior through the abstract science and idealization. Therefore, it is discredited to extend the principles of quantum mechanics to human being's progress and learning. Qua...

The author discusses a different kind of Hermitian quantum mechanics, called $J$-Hermitian quantum mechanics. He shows that $PT$-symmetric quantum mechanics is indeed $J$-Hermitian quantum mechanics, and that time evolution (in the Krein space of states) is unitary if and only if Hamiltonian is $J$-Hermitian (or equivalently $PT$-symmetric). An issue with unitarity comes up when time evolution is considered in the Hilbert space of states rather than in the Krein space of states. The author offers possible scenarios with this issue.

§1 Recall and discuss There were several experiments which pointed to inadequacy of the classical thoeries such as mechanics,electromagnetic theory of light, and statistical mechanics. Here we list some of the important experimental facts which had no explanation within the classical theories. 1. Black Body radiation 2. Photoelectric effect 3. Atomic spectra 4. Frank Hertz experiment 5. Compton effect

A condition for approximate decoherence is proposed, and it is argued that most probability sum rules will be satisfied to approximately the same degree, and an inequality bounding the size of the off-diagonal terms of thedecoherence functional is derived.

We discuss the relation between our approach to quantum mechanics, based on coarsegrained decoherent histories of a closed system, and the approximate quantum mechanics of measured subsystems, as in the “Copenhagen interpretation.” The latter formulation postulates (implicitly for most authors or explicitly in the case of Landau and Lifshitz [1]) a classical world and a quantum world, with a movable boundary between the two. Observers and their measuring apparatus make use of the classical world, so that the results of a “measurement” are ultimately expressed in one or more “c-numbers”. We hav...

We showed in a recent article (Lawrence et. al., 2023, Quantum 7, 1015), that relative facts (outcomes), a central concept in Relational Quantum Mechanics, are inconsistent with Quantum Mechanics. We proved this by constructing a Wigner-Friend type sequential measurement scenario on a Greenberger-Horne-Zeilinger (GHZ) state of three qubits, and making the following assumption:"if an interpretation of quantum theory introduces some conceptualization of outcomes of a measurement, then probabilities of these outcomes must follow the quantum predictions as given by the Born rule."Our work has been...

Some examples in new quantum mechanics with the Riemannian energy-momentum space are described.

The Ultra Violet Catastrophe In blackbody spectra, the spectral distribution of energy in the radiation depends only on the temperature of the body. Why does the blackbody spectrum have the shape it has? Lord rayleigh and James Jean considered the radiation inside a cavity of absolute temperature T whose walls are perfect reflectors to be a series of standing electromagnetic waves. This is a three dimensional generalization of standing waves in a stretched string. The condition for standing waves in such a cavity is that the path length from wall to wall, whatever the location, must be a while...

Das Buch ist in einer dritten, v ̈ ollig überarbeiteten Auflage erschienen. Es ist als Begleitung eines wenigstens einj ̈ ahrigen Kurses gedacht und wendet sich an Studenten, die Vordiplomskenntnisse in Mechanik, Elektrodynamik sowie Atomphysik besitzen. Die Quantenmechnik wird in ihrer ganzen Breite behandelt. Das Buch beginnt mit der Wellenmechanik, der ein sehr großer Platz einger ̈ aumt und auf die immer wieder zurückgegriffen wird. Freie Bewegung, harmonischer Oszillator, st ̈ uckweise konstante Potentiale werden ausf ̈ uhrlich behandelt. Ebenso detailreich werden N ̈ aherungsverfahren wi...

We discuss the axiomatic basis of quantum mechanics and show that it is neither general nor consistent, since its axioms are incompatible with each other and moreover it does not incorporate the magnetic quantization as in the cyclotron motion. A general and consistent system of axioms is conjectured which incorporates also the magnetic quantization.

We reformulate the problem of the "interpretation of quantum mechanics" as the problem of DERIVING the quantum mechanical formalism from a set of simple physical postulates. We suggest that the common unease with taking quantum mechanics as a fundamental description of nature could derive from the use of an incorrect notion, as the unease with the Lorentz transformations before Einstein derived from the notion of observer independent time. Following an an analysis of the measurement process as seen by different observers, we propose a reformulation of quantum mechanics in terms of INFORMATION ...

This popular undergraduate quantum mechanics textbook is now available in a more affordable printing from Cambridge University Press. Unlike many other books on quantum mechanics, this text begins by examining experimental quantum phenomena such as the Stern-Gerlach experiment and spin measurements, using them as the basis for developing the theoretical principles of quantum mechanics. Dirac notation is developed from the outset, offering an intuitive and powerful mathematical toolset for calculation, and familiarizing students with this important notational system. This non-traditional approa...

This original and innovative textbook takes the unique perspective of introducing and solving problems in quantum mechanics using linear algebra methods, to equip readers with a deeper and more practical understanding of this fundamental pillar of contemporary physics. Extensive motivation for the properties of quantum mechanics, Hilbert space, and the Schrödinger equation is provided through analysis of the derivative, while standard topics like the harmonic oscillator, rotations, and the hydrogen atom are covered from within the context of operator methods. Advanced topics forming the basi...

challenging because a quantum phenomenon is counterintuitive and the mathematics used to explain it is often abstract and dif cult to grasp. This textbook is an attempt to overcome these challenges. Every chapter presents quantum ideas in a stepbystep structured way along with comparisons between quantum and classical concepts that provide clear distinction between classical and quantum logic. Conceptual questions are given after every important section so that readers can check their understanding at every step. Tutorials are included on special topics to teach problem solving by actively eng...

The important changes quantum mechanics has undergone in recent years are reflected in this new approach for students. A strong narrative and over 300 worked problems lead the student from experiment, through general principles of the theory, to modern applications. Stepping through results allows students to gain a thorough understanding. Starting with basic quantum mechanics, the book moves on to more advanced theory, followed by applications, perturbation methods and special fields, and ending with new developments in the field. Historical, mathematical, and philosophical boxes guide the st...

Quantum mechanics (QM) is the modern physical theory of very small (microscopic) systems, typically atomic-sized or smaller. Along with Einstein's theory of relativity, QM represented a major revolution in our understanding of physics, which was previously described by Newtonian (classical) mechanics. Problems with Classical Physics The enormous success of Newtonian mechanics led Lord Kelvin to state the following in 1894 [2]: " There is nothing new to be discovered in physics now. All that remains is more and more precise measurement. " How wrong he was! However, it seemed that way for many p...

Written for a two-semester graduate course in Quantum Mechanics, this comprehensive text helps develop the tools and formalism of Quantum Mechanics and its applications to physical systems. It suits students who have taken some introductory Quantum Mechanics and Modern Physics courses at undergraduate level, but it is self-contained and does not assume any specific background knowledge beyond appropriate fluency in mathematics. The text takes a modern logical approach rather than a historical one and it covers standard material, such as the hydrogen atom and the harmonic oscillator, the WKB ap...

Quantum mechanics (QM – also known as quantum physics, or quantum theory) is a branch of physicswhich deals with physical phenomena at microscopic scales, where the action is on the order of the Planck constant. Quantum mechanics departs from classical mechanics primarily at the quantum realm of atomic andsubatomic length scales. Quantum mechanics provides a mathematical description of much of the dual particle-likeand wavelike behavior and interactions of energy andmatter.

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There are two supposed equivalent versions of the quantum mechanics: the matrix mechanics and the wave mechanics. I think that both would be false.

The recently published theoretical approach of Heisenberg is here developed into a systematic theory of quantum mechanics (in the first place for systems having one degree of freedom) with the aid of mathematical matrix methods. After a brief survey of the latter, the mechanical equations of motion are derived from a variational principle and it is shown that using Heisenberg’s quantum condition, the principle of energy conservation and Bohr’s frequency condition follow from the mechanical equations. Using the anharmonic oscillator as example, the question of uniqueness of the solution and of ...

Designed for a two-semester advanced undergraduate or graduate level course, this distinctive and modern textbook provides students with the physical intuition and mathematical skills to tackle even complex problems in quantum mechanics with ease and fluency. Beginning with a detailed introduction to quantum states and Dirac notation, the book then develops the overarching theoretical framework of quantum mechanics, before explaining physical quantum mechanical properties such as angular momentum and spin. Symmetries and groups in quantum mechanics, important components of current research, ar...

Article 1. Quantum Mechanics/量子力学 Author: Liu Huan (1983- ), Master of Science (First Class Honours), The University of Auckland.

This is an advanced course in the theory of quantum mechanics, for junior or senior level students. It is intended primarily for physics majors, but should be of interest also to many other students, especially those in math, science and engineering. Prerequisite are PHY 305 Modern Physics I, MAT 293 Multivariable Calculus, and MAT 330 Introduction to Differential Equations. Students are therefore assumed to know some basic quantum physics, and to be able to use vector calculus and simple differential equations. They will learn the mathematical formalism of quantum mechanics, its application t...

I consider in this book a formulation of Quantum Mechanics. Usually QM is formulated based on the notion of time and space, both of which are thought a priori given quantities or notions. However, when we try to define the notion of velocity or momentum, we encounter a difficulty as we will see in chapter 1. The problem is that if the notion of time is given a priori, the velocity is definitely determined when given a position, which contradicts the uncertainty principle of Heisenberg. We then set the basis of QM on the notion of position and momentum operators as in chapter 2. Time of a local...

From the Publisher: This book provides an introduction to the theoretical foundations of quantum mechanics for students of experimental physics. It is intended as an intermediate text for those who have already completed an introductory course in quantum physics.

This book explains the often counterintuitive physics of quantum mechanics, unlocking this key area of physics for students by enabling them to work through detailed applications of general concepts and ideas. The book states general principles first in terms of wave mechanics and then in the standard abstract linear space formalism. It offers a detailed discussion of measurement theory — an essential feature of quantum mechanics — and emphasizes the art of numerical estimates. Along the way, the book provides a wealth of physical examples together with numerous problems, some easy, some chall...

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This book provides a comprehensive account of basic concepts of quantum mechanics in a coherent manner. The book is self-contained and not only covers basic concepts in quantum mechanics but also provides a basis for applications in atomic and laser physics, nuclear and particle physics, and condensed matter physics. It also covers relativistic quantum mechanics, in particular the Dirac equation and its applications.

The controlled generation and verification of quantum entanglement of a mesoscopic mechanical device (a mechanical oscillator) with an electromagnetic microwave field is reported.

The Newton equation of motion is derived from quantum mechanics.

Nanoelectromechanical structures are starting to approach the ultimate quantum mechanical limits for detecting and exciting motion at the nanoscale. Nonclassical states of a mechanical resonator are also on the horizon.

There is great interest in “emergent” dynamical systems and the possibility of quantum mechanics as emergent phenomena. We engage the topic by making a sharp distinction between models of microphysics, and the so-called quantum framework. We find the models have all the information. Given that the framework of quantum theory is mathematically self-consistent we propose it should be viewed as an information management tool not derived from physics nor depending on physics. That encourages practical applications of quantum-style information management to near arbitrary data systems. As part of d...

James kakalios sets out to be, used we take the electron and matter has. So mysterious and partial differential hence no. And that you can call a justification in the fundamental rules. I can only have those predictions held up you're confused. Quantum mechanics was going to absorb some ideas in the university. And manipulate them that we live, in a little mezzanine by it good. To buy a certificate with an, expression quantum mechanics make level. The quantum mechanics is a textbook, the states high and said. There is thrown around there, would lead to another you went. You accept on a more th...

This book is dedicated to the non-Hermitian formalism of quantum mechanics. In this chapter we wish to give the motivation and the rational for developing a non-Hermitian formalism to quantum mechanics. Therefore this chapter will not explain how non-Hermitian calculations are carried out or in what way the non-Hermitian formalism is analogous to the standard (Hermitian) formalism of quantum mechanics. It is important to emphasize that there is no (known) transformation which enables one to map results which were obtained using one formalism to the other one. Yet, the same physical results sho...

Before attempting to investigate theworkings of a tunnelling field-effect transistor, it is essential to be familiarwith the concept of tunnelling. Tunnelling is a quantumphenomenon,with no counterpart in the everyday physics one encounters, or the physics that one applies while dealing with devices a few hundred nanometres in length. The initial two chapterswill, therefore, help us develop an understanding of quantumphenomena. In this chapter,wewill present an introduction to the field of quantummechanics and the next chapter will discuss the phenomenon of tunnelling in detail. The chapter be...