quantum physics

@kaniam (582)
December 22, 2006 8:34am CST
Quantum mechanics is a fundamental branch of theoretical physics with wide applications in experimental physics that replaces classical mechanics and classical electromagnetism at the atomic and subatomic levels. It is the underlying mathematical framework of many fields of physics and chemistry, including condensed matter physics, atomic physics, molecular physics, computational chemistry, quantum chemistry, particle physics, and nuclear physics. Along with general relativity, quantum mechanics is one of the pillars of modern physics. For a non-technical introduction to the topic, please see Introduction to quantum mechanics. Quantum series Introduction Introduction to quantum mechanics Quantum mechanics Quantum theory Mathematical formulation of quantum mechanics Fundamental Concepts Transformation theory Quantum decoherence Ehrenfest theorem Interference Exclusion principle Uncertainty principle Scientists Werner Heisenberg Wolfgang Pauli Max Planck Louis de Broglie Niels Bohr Erwin Schrödinger Max Born John von Neumann Paul Dirac Albert Einstein Richard Feynman Hugh Everett others Laws & Equations Schrödinger equation Dirac equation Klein-Gordon equation Advanced Theories Quantum field theory Quantum electrodynamics Quantum chromodynamics Quantum gravity Feynman diagram Sub-atomic Particules electron proton gluon graviton neutron quark muon Interpretations Copenhagen Interpretation Quantum logic Hidden variables Transactional interpretation Many-worlds interpretation Ensemble Interpretation Consistent histories Consciousness causes collapse Relational quantum mechanics Orchestrated Objective Reduction This box: view • talk • edit Contents[hide] 1 Introduction 2 Theory 2.1 Mathematical formulation 2.2 Interactions with other scientific theories 3 Applications 4 Philosophical consequences 5 History 5.1 Founding experiments 6 See also 7 References 8 Footnote 9 External links [edit] Introduction Main article: Introduction to quantum mechanics The term quantum (Latin, "how much") refers to discrete units that the theory assigns to certain physical quantities, such as the energy of an atom at rest (see Figure 1, at right). The discovery that waves could be measured in particle-like small packets of energy called quanta led to the branch of physics that deals with atomic and subatomic systems which we today call Quantum Mechanics. The foundations of quantum mechanics were established during the first half of the twentieth century by Werner Heisenberg, Max Planck, Louis de Broglie, Niels Bohr, Erwin Schrödinger, Max Born, John von Neumann, Paul Dirac, Albert Einstein, Wolfgang Pauli and others. Some fundamental aspects of the theory are still actively studied. Quantum mechanics is a more fundamental theory than Newtonian mechanics and classical electromagnetism, in the sense that it provides accurate and precise descriptions for many phenomena that these "classical" theories simply cannot explain on the atomic and subatomic level. It is necessary to use quantum mechanics to understand the behavior of systems at atomic length scales and smaller. For example, if Newtonian mechanics governed the workings of an atom, electrons would rapidly travel towards and collide with the nucleus. However, in the natural world the electron normally remains in a stable orbit around a nucleus — seemingly defying classical electromagnetism. Quantum mechanics was initially developed to explain the atom, especially the spectra of light emitted by different atomic species. The quantum theory of the atom developed as an explanation for the electron's staying in its orbital, which could not be explained by Newton's laws of motion and by classical electromagnetism. In the formalism of quantum mechanics, the state of a system at a given time is described by a complex wave function (sometimes referred to as orbitals in the case of atomic electrons), and more generally, elements of a complex vector space. This abstract mathematical object allows for the calculation of probabilities of outcomes of concrete experiments. For example, it allows one to compute the probability of finding an electron in a particular region around the nucleus at a particular time. Contrary to classical mechanics, one cannot ever make simultaneous predictions of conjugate variables, such as position and momentum, with arbitrary accuracy. For instance, electrons may be considered to be located somewhere within a region of space, but with their exact positions being unknown. Contours of constant probability, often referred to as “clouds” may be drawn around the nucleus of an atom to conceptualise where the electron might be located with the most probability. It should be stressed that the electron itself is not spread out over such cloud regions. It is either in a particular region of space, or it is not. Heisenberg's uncertainty principle quantifies the inability to precisely locate the particle. The other exemplar that led to quantum mechanics was the study of electromagnetic waves such as light. When it was found in 1900 by Max Planck that the energy of waves could be described as consisting of small packets or quanta, Albert Einstein exploited this idea to show that an electromagnetic wave such as light could be described by a particle called the photon with a discrete energy dependent on its frequency. This led to a theory of unity between subatomic particles and electromagnetic waves called wave-particle duality in which particles and waves were neither one nor the other, but had certain properties of both. While quantum mechanics describes the world of the very small, it also is needed to explain certain "macroscopic quantum systems" such as superconductors and superfluids. Broadly speaking, quantum mechanics incorporates four classes of phenomena that classical physics cannot account for: (i) the quantization (discretization) of certain physical quantities, (ii) wave-particle duality, (iii) the uncertainty principle, and (iv) quantum entanglement. Each of these phenomena will be described in greater detail in subsequent sections. Since the early days of quantum theory, physicists have made many attempts to combine it with the other highly successful theory of the twentieth century, Albert Einstein's General Theory of Relativity. While quantum mechanics is entirely consistent with special relativity, serious problems emerge when one tries to join the quantum laws with general relativity, a more elaborate description of spacetime which incorporates gravitation. Resolving these inconsistencies has been a major goal of twentieth- and twenty-first-century physics. Despite the proposal of many novel ideas, the unification of quantum mechanics—which reigns in the domain of the very small—and general relativity—a superb description of the very large—remains a tantalizing future possibility. (See quantum gravity, string theory.) Because everything is composed of quantum-mechanical particles, the laws of classical physics must approximate the laws of quantum mechanics in the appropriate limit. This is often expressed by saying that in case of large quantum numbers quantum mechanics "reduces" to classical mechanics and classical electromagnetism. This requirement is called the correspondence, or classical limit. [edit] Theory There are numerous mathematically equivalent formulations of quantum mechanics. One of the oldest and most commonly used formulations is the transformation theory invented by Cambridge theoretical physicist Paul Dirac, which unifies and generalizes the two earliest formulations of quantum mechanics, matrix mechanics (invented by Werner Heisenberg)[1] and wave mechanics (invented by Erwin Schrödinger). In this formulation, the instantaneous state of a quantum system encodes the probabilities of its measurable properties, or "observables". Examples of observables include energy, position, momentum, and angular momentum. Observables can be either continuous (e.g., the position of a particle) or discrete (e.g., the energy of an electron bound to a hydrogen atom). Generally, quantum mechanics does not assign definite values to observables. Instead, it makes predictions about probability distributions; that is, the probability of obtaining each of the possible outcomes from measuring an observable. Naturally, these probabilities will depend on the quantum state at the instant of the measurement. There are, however, certain states that are associated with a definite value of a particular observable. These are known as "eigenstates" of the observable ("eigen" meaning "own" in German). In the everyday world, it is natural and intuitive to think of everything being in an eigenstate of every observable. Everything appears to have a definite position, a definite momentum, and a definite time of occurrence. However, quantum mechanics does not pinpoint the exact values for the position or momentum of a certain particle in a given space in a finite time, but, rather, it only provides a range of probabilities of where that particle might be. Therefore, it became necessary to use different words for a) the state of something having an uncertainty relation and b) a state that has a definite value. The latter is called the "eigenstate" of the property being measured. A concrete example will be useful here. Let us consider a free particle. In quantum mechanics, there is wave-particle duality so the properties of the particle can be described as a wave. Therefore, its quantum state can be represented as a wave, of arbitrary shape and extending over all of space, called a wavefunction. The position and momentum of the particle are observables. The Uncertainty Principle of quantum mechanics states that both the position and the momentum cannot simultaneously be known with infinite precision at the same time. However, we
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