Quantum mechanics is a fundamental physical theory that replaces Newtonian mechanics and classical electromagnetism at the atomic and subatomic levels and is the underlying framework of many fields of physics and chemistry, including condensed matter physics, quantum chemistry, and particle physics. Along with general relativity, it is one of the pillars of modern physics. Quantum mechanics - Introduction. The term quantum (Latin, "how much") refers to the discrete units that the theory assign ...

Including:

• Quantum mechanics - Introduction
• Quantum mechanics - Description of the theory
• Quantum mechanics - Quantum mechanical effects
• Quantum mechanics - Mathematical formulation
• Quantum mechanics - Interactions with other scientific theories
• Quantum mechanics - Applications of quantum theory
• Quantum mechanics - Philosophical consequences
• Quantum mechanics - History
• Quantum mechanics - Founding experiments
• Quantum mechanics - Notes

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Including:

• Basics of quantum mechanics - Background
• Basics of quantum mechanics - Old quantum theory
• Basics of quantum mechanics - Planck's constant
• Basics of quantum mechanics - Reduced Planck's constant
• Basics of quantum mechanics - Bohr atom
• Basics of quantum mechanics - Wave-particle duality
• Basics of quantum mechanics - Development of modern quantum mechanics
• Basics of quantum mechanics - Full quantum mechanical theory
• Basics of quantum mechanics - Schrödinger wave equation
• Basics of quantum mechanics - Uncertainty Principle
• Basics of quantum mechanics - Wavefunction collapse
• Basics of quantum mechanics - Eigenstates and eigenvalues
• Basics of quantum mechanics - The Pauli Exclusion Principle
• Basics of quantum mechanics - Dirac wave equation
• Basics of quantum mechanics - Quantum entanglement
• Basics of quantum mechanics - Notes

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The term quantum (Latin, "how much") refers to the 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 20th century by Max Planck, Albert Einstein, Niels Bo ...

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Quantum mechanics, Quantum mechanics - Introduction, Quantum mechanics - Description of the theory, Quantum mechanics - Quantum mechanical effects, Quantum mechanics - Mathematical formulation, Quantum mechanics - Interactions with other scientific theories, Quantum mechanics - Applications of quantum theory, Quantum mechanics - Philosophical consequences, Quantum mechanics - History, Quantum mechanics - Founding experiments, Quantum mechanics - Notes

Read more here: » Quantum mechanics: Encyclopedia II - Quantum mechanics - Introduction

In quantum mechanics, spacetime transformations act on quantum states. The parity transformation, P, becomes an unitary operator in quantum mechanics, acting on a wavefunction ψ as follows: Pψ(r)  =  ψ(-r). Clearly, one must have P2ψ(r)=eiφψ(r), since an overall phase is unobservable. Then one can remove this complication by choosing φ=0. With this redefinition of the operator P we get the relation P2=1< ...

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Parity physics, Parity physics - Simple symmetry relations, Parity physics - Classical mechanics, Parity physics - Quantum mechanics, Parity physics - Quantum field theory, Parity physics - Parity violation, Parity physics - Intrinsic parity of hadrons

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As a student, he met Niels Bohr in Göttingen in 1922. A fruitful collaboration developed between the two. He invented matrix mechanics, the first formalization of quantum mechanics in 1925. His uncertainty principle, discovered in 1927, states that the simultaneous determination of both the position and momentum of a particle each has an inherent uncertainty, the product of these being not less than a known constant. Together with Bohr, he would go on to formul ...

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Werner Heisenberg, Werner Heisenberg - Life, Werner Heisenberg - Quantum mechanics, Werner Heisenberg - Work during the War, Werner Heisenberg - Looking back

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In quantum mechanics, the conservation of probability also yields a continuity equation. Let P(x, t) be a probability density and write where J is probability flux. ...

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Continuity equation, Continuity equation - Electromagnetic theory, Continuity equation - Derivation, Continuity equation - Interpretation, Continuity equation - Fluid dynamics, Continuity equation - Quantum mechanics

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In the classical mechanics of a particle one has dynamical variables which are called coordinates (q) and momenta (p). These specify the state of a classical system. The canonical structure (also known as the symplectic structure) of classical mechanics consists of Poisson brackets between these variables. All transformations which keep these brackets unchanged are allowed as canonical transformations in classical mechanics. In quantum mechanics, these dynamical variables become operators acting on a Hilber ...

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Canonical quantization, Canonical quantization - History, Canonical quantization - Quantum mechanics, Canonical quantization - Second quantization: field theory, Canonical quantization - Field operator, Canonical quantization - Condensates, Canonical quantization - Why canonical?, Canonical quantization - Mathematical quantization

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At the International Congress of Mathematicians of 1900, David Hilbert presented his famous list of twenty-three problems considered central for the development of the mathematics of the new century: the sixth of these was the axiomatization of physical theories. Among the new physical theories of the century the only one which had yet to receive such a treatment by the end of the 1930's was quantum mechanics. In fact, QM found itself, at this time, in a condition of foundational crisis similar to that of set theory at the beginning o ...

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John von Neumann, John von Neumann - Biography, John von Neumann - Logic, John von Neumann - Quantum mechanics, John von Neumann - Economics, John von Neumann - Armaments, John von Neumann - Computer science, John von Neumann - Politics and social affairs, John von Neumann - Honors, John von Neumann - Students

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Bra-ket notation | Commutation relation | Heisenberg picture | Schrödinger picture | Wavefunction | Measurement in quantum mechanics | Semiclassical | Path integral | WKB approximation | Quantum logic | Quantum operation | Quantum field theory | Wightman axioms | Statistical ensemble | Wigner quasi-probability distribution Matrix mechanics, Hamiltonian | Particle in a box | Particle in a ring | Particle in a spherically symmetric potential | Quantum harmonic oscillator | Hydrogen ...

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Quantum mechanics, Quantum mechanics - Introduction, Quantum mechanics - Description of the theory, Quantum mechanics - Quantum mechanical effects, Quantum mechanics - Mathematical formulation, Quantum mechanics - Interactions with other scientific theories, Quantum mechanics - Applications of quantum theory, Quantum mechanics - Philosophical consequences, Quantum mechanics - History, Quantum mechanics - Founding experiments, Quantum mechanics - Notes

Read more here: » Quantum mechanics: Encyclopedia II - Quantum mechanics - Description of the theory

The word quantum, pl. "quanta", comes from the Latin "quantus", for "how much". In general, it refers to an "amount of something". But, the term is often used in the more specific sense which it has in physics, where a quantum refers to an indivisible, and perhaps elementary entity. For instance, a "light quantum", being a unit of light (that is, a photon). In combinations like "quantum mechanics", "quantum optics", etc., it di ...

Including:

• Quantum - Discovery of quantum theory
• Quantum - The quantum black-body radiation formula
• Quantum - The birthday of quantum mechanics
• Quantum - Quantization in antiquity

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The wave packet is one of the most widely misunderstood and misused concepts in physics. In general, a wave packet is an envelope or packet containing an arbitrary number of wave forms. This is also true in quantum mechanics, however in this case the wave packet is ascribed a special significance. In quantum mechanics the wave packet is interpreted to be a "probability wave" describing the probability that a particu ...

Including:

• Wave packet - Background
• Wave packet - Quantum mechanical waves
• Wave packet - Superposition
• Wave packet - The collapse of the wave packet
• Wave packet - Metaphysical claims

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In quantum field theory, the vacuum state (also called the vacuum) is the quantum state with the lowest possible energy. As a result, it contains no physical particles. Conventionally it has zero energy (see however cosmological constant). For a relativistic field theory, the vacuum is Poincaré invariant. If the field theory can be accurately described through perturbation theory, then the properties of the vacuum are analogous to the properties of the ground state of a quantum mechanical harmonic oscillator. In this ca ...

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In physics, classical mechanics or Newtonian mechanics is one of the two major sub-fields of study in the science of mechanics, which is concerned with the set of physical laws governing and mathematically describing the motions of bodies and aggregates of bodies. The other sub-field is quantum mechanics. The term classical mechanics was coined in the early 20th century to describe the system of mathematical physics developed in the 400 years since the groundbreaking works of Brahe, Kepler, and Galileo,but before the dev ...

Including:

• Classical mechanics - Description of the theory
• Classical mechanics - Position and its derivatives
• Classical mechanics - Forces; Newton's second law
• Classical mechanics - Energy
• Classical mechanics - Beyond Newton's Laws
• Classical mechanics - Classical transformations
• Classical mechanics - History
• Classical mechanics - Limits of validity
• Classical mechanics - The classical approximation to special relativity
• Classical mechanics - The classical approximation to quantum mechanics
• Classical mechanics - Notes

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In quantum mechanics a coherent state is a specific kind of quantum state of the quantum harmonic oscillator whose dynamics most closely resemble the oscillating behaviour of a classical harmonic oscillator system. It was the first example of quantum dynamics when Erwin Schrödinger derived it in 1926 while searching for solutions of the Schrödinger equation that satisfy the correspondence principle. The quantum harmonic oscillator and hence, the coherent state, arise in the quantum theory of a wide range of physical systems. For ins ...

Including:

• Coherent state - Coherent states in quantum optics
• Coherent state - Quantum mechanical definition
• Coherent state - Mathematical characteristics
• Coherent state - Coherent states of Bose-Einstein condensates
• Coherent state - Generalizations

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Basics of quantum mechanics - Full quantum mechanical theory. Werner Heisenberg developed the full quantum mechanical theory in 1925 at the young age of 23. Following his mentor, Niels Bohr, Werner Heisenberg began to work out a theory for the quantum behavior of electron orbitals. Because electron orbits could not be observed, Heisenberg went about creating a mathematical description of quantum mechanics built on what could be observed, that is, the light emitted from atoms in their atomic spectrum. When a pure ...

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Basics of quantum mechanics, Basics of quantum mechanics - Background, Basics of quantum mechanics - Old quantum theory, Basics of quantum mechanics - Planck's constant, Basics of quantum mechanics - Reduced Planck's constant, Basics of quantum mechanics - Bohr atom, Basics of quantum mechanics - Wave-particle duality, Basics of quantum mechanics - Development of modern quantum mechanics, Basics of quantum mechanics - Full quantum mechanical theory, Basics of quantum mechanics - Schrödinger wave equation, Basics of quantum mechanics - Uncertainty Principle, Basics of quantum mechanics - Wavefunction collapse, Basics of quantum mechanics - Eigenstates and eigenvalues, Basics of quantum mechanics - The Pauli Exclusion Principle, Basics of quantum mechanics - Dirac wave equation, Basics of quantum mechanics - Quantum entanglement, Basics of quantum mechanics - Notes

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The perceived difficulties of interpretation reflect a number of points about the orthodox description of quantum mechanics. In this article we point out four of these points: The abstract, mathematical nature of the description of quantum mechanics. The existence of non-deterministic and irreversible processes in quantum mechanics. The phenomenon of entanglement, and in particular, the higher correlations between remote events than would be expected ...

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Interpretation of quantum mechanics, Interpretation of quantum mechanics - Historical background, Interpretation of quantum mechanics - Obstructions to direct interpretation, Interpretation of quantum mechanics - Problematic status of pictures and interpretations, Interpretation of quantum mechanics - Instrumentalist interpretation, Interpretation of quantum mechanics - Properties of interpretations, Interpretation of quantum mechanics - Quantum Logic, Interpretation of quantum mechanics - Consciousness causes collapse, Interpretation of quantum mechanics - Comparison, Interpretation of quantum mechanics - Related lists

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Through over fifty years of experimentation and applied science, quantum mechanical theory has proven to be very successful and practical. The term "quantum mechanics" was first coined by Max Born in 1924. Quantum mechanics is the foundation for other sciences including condensed matter physics, quantum chemistry, and particle physics. Despite the success of quantum mechanics, it does have some controversial elements. For example, the behaviour of microscopic objects described in quantum mechanics is very different from our everyday e ...

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Basics of quantum mechanics, Basics of quantum mechanics - Background, Basics of quantum mechanics - Old quantum theory, Basics of quantum mechanics - Planck's constant, Basics of quantum mechanics - Reduced Planck's constant, Basics of quantum mechanics - Bohr atom, Basics of quantum mechanics - Wave-particle duality, Basics of quantum mechanics - Development of modern quantum mechanics, Basics of quantum mechanics - Full quantum mechanical theory, Basics of quantum mechanics - Schrödinger wave equation, Basics of quantum mechanics - Uncertainty Principle, Basics of quantum mechanics - Wavefunction collapse, Basics of quantum mechanics - Eigenstates and eigenvalues, Basics of quantum mechanics - The Pauli Exclusion Principle, Basics of quantum mechanics - Dirac wave equation, Basics of quantum mechanics - Quantum entanglement, Basics of quantum mechanics - Notes

Read more here: » Basics of quantum mechanics: Encyclopedia II - Basics of quantum mechanics - Background

Quantum mechanics developed from the study of electromagnetic waves through spectroscopy which includes visible light seen in the colors of the rainbow, but also other waves including the more energetic waves like ultraviolet light, x-rays, and gamma rays plus the waves with longer wavelengths including infrared waves, microwaves and radio waves. We are not, however, speaking of sound waves, but only of those waves that travel at the speed of light. Also, when the word "particle" is used below, it always refers to elementary or subatomic particles. ...

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Basics of quantum mechanics, Basics of quantum mechanics - Background, Basics of quantum mechanics - Old quantum theory, Basics of quantum mechanics - Planck's constant, Basics of quantum mechanics - Reduced Planck's constant, Basics of quantum mechanics - Bohr atom, Basics of quantum mechanics - Wave-particle duality, Basics of quantum mechanics - Development of modern quantum mechanics, Basics of quantum mechanics - Full quantum mechanical theory, Basics of quantum mechanics - Schrödinger wave equation, Basics of quantum mechanics - Uncertainty Principle, Basics of quantum mechanics - Wavefunction collapse, Basics of quantum mechanics - Eigenstates and eigenvalues, Basics of quantum mechanics - The Pauli Exclusion Principle, Basics of quantum mechanics - Dirac wave equation, Basics of quantum mechanics - Quantum entanglement, Basics of quantum mechanics - Notes

Read more here: » Basics of quantum mechanics: Encyclopedia II - Basics of quantum mechanics - Old quantum theory

Measurement in quantum mechanics - Measurable quantities observables as operators. An observable quantity is represented mathematically by a Hermitian operator. The set of the operator's eigenvalues represent the set of possible definite result values which might be obtained as a result of the measurement. For each eigenvalue there is a corresponding eigenstate (or "eigenvector"), which will be the state of the system after the measurement. This representation is possible and appropriate because Its ...

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Measurement in quantum mechanics, Measurement in quantum mechanics - The mathematical formalism of measurement, Measurement in quantum mechanics - Measurable quantities observables as operators, Measurement in quantum mechanics - Eigenstates and projection, Measurement in quantum mechanics - Wavefunction collapse, Measurement in quantum mechanics - von Neumann measurement scheme, Measurement in quantum mechanics - Example, Measurement in quantum mechanics - Philosophical problems of quantum measurements, Measurement in quantum mechanics - What physical interaction constitutes a measurement?, Measurement in quantum mechanics - Does measurement actually determine the state?, Measurement in quantum mechanics - The quantum entanglement problem

Read more here: » Measurement in quantum mechanics: Encyclopedia II - Measurement in quantum mechanics - The mathematical formalism of measurement

Measurement in quantum mechanics - What physical interaction constitutes a measurement?. Until the advent of quantum decoherence theory in the late 20th century, a major conceptual problem of quantum mechanics and especially the Copenhagen interpretation was the lack of a distinctive criterion for a given physical interaction to qualify as "a measurement" and cause a wavefunction to collapse. This best illustrated by the Schrödinger's cat paradox. Major philosophical and metaphysical questions surround th ...

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Measurement in quantum mechanics, Measurement in quantum mechanics - The mathematical formalism of measurement, Measurement in quantum mechanics - Measurable quantities observables as operators, Measurement in quantum mechanics - Eigenstates and projection, Measurement in quantum mechanics - Wavefunction collapse, Measurement in quantum mechanics - von Neumann measurement scheme, Measurement in quantum mechanics - Example, Measurement in quantum mechanics - Philosophical problems of quantum measurements, Measurement in quantum mechanics - What physical interaction constitutes a measurement?, Measurement in quantum mechanics - Does measurement actually determine the state?, Measurement in quantum mechanics - The quantum entanglement problem

Read more here: » Measurement in quantum mechanics: Encyclopedia II - Measurement in quantum mechanics - Philosophical problems of quantum measurements