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Non-linear Coherent States
Coherent states are quasi-classical states that may be defined in different ways, for instance as eigenstates of the annihilation operator : a, \alpha\rangle=\alpha, \alpha\rangle, or as a displacement from the vacuum : , \alpha\rangle=D(\alpha), 0\rangle, where D(\alpha)=\exp(\alpha a^-\alpha^* a) is the Sudarshan-Glauber displacement operator. One may think of a non-linear coherent state by generalizing the annihilation operator: : A=af(a^a), and then using any of the above definitions by exchanging a by A . The above definition is also known as an f-deformed annihilation operator Creation operators and annihilation operators are mathematical operators that have widespread applications in quantum mechanics, notably in the study of quantum harmonic oscillators and many-particle systems. An annihilation operator (usually d ....V. I. Man'ko, G. Marmo, F. Zaccaria and E. C. G. Sudarshan, Proceedings of the IV Wigner Symposium, eds. N. Atakishiyev, T. Seligman and K. B. W ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coherent States
In physics, specifically in quantum mechanics, a coherent state is the specific quantum state of the quantum harmonic oscillator, often described as a state which has dynamics most closely resembling the oscillatory behavior of a classical harmonic oscillator. 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 states) arise in the quantum theory of a wide range of physical systems.J.R. Klauder and B. Skagerstam, ''Coherent States'', World Scientific, Singapore, 1985. For instance, a coherent state describes the oscillating motion of a particle confined in a quadratic potential well (for an early reference, see e.g. Schiff's textbook). The coherent state describes a state in a system for which the ground-state wavepacket is displaced from the origin of the system. This state can be rela ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eigenstates
In quantum physics, a quantum state is a mathematical entity that provides a probability distribution for the outcomes of each possible measurement on a system. Knowledge of the quantum state together with the rules for the system's evolution in time exhausts all that can be predicted about the system's behavior. A mixture of quantum states is again a quantum state. Quantum states that cannot be written as a mixture of other states are called pure quantum states, while all other states are called mixed quantum states. A pure quantum state can be represented by a ray in a Hilbert space over the complex numbers, while mixed states are represented by density matrices, which are positive semidefinite operators that act on Hilbert spaces. Pure states are also known as state vectors or wave functions, the latter term applying particularly when they are represented as functions of position or momentum. For example, when dealing with the energy spectrum of the electron in a hydrogen a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Annihilation Operator
Creation operators and annihilation operators are mathematical operators that have widespread applications in quantum mechanics, notably in the study of quantum harmonic oscillators and many-particle systems. An annihilation operator (usually denoted \hat) lowers the number of particles in a given state by one. A creation operator (usually denoted \hat^\dagger) increases the number of particles in a given state by one, and it is the adjoint of the annihilation operator. In many subfields of physics and chemistry, the use of these operators instead of wavefunctions is known as second quantization. They were introduced by Paul Dirac. Creation and annihilation operators can act on states of various types of particles. For example, in quantum chemistry and many-body theory the creation and annihilation operators often act on electron states. They can also refer specifically to the ladder operators for the quantum harmonic oscillator. In the latter case, the raising operator is inte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vacuum State
In quantum field theory, the quantum vacuum state (also called the quantum vacuum or vacuum state) is the quantum state with the lowest possible energy. Generally, it contains no physical particles. The word zero-point field is sometimes used as a synonym for the vacuum state of a quantized field which is completely individual. According to present-day understanding of what is called the vacuum state or the quantum vacuum, it is "by no means a simple empty space". According to quantum mechanics, the vacuum state is not truly empty but instead contains fleeting electromagnetic waves and particles that pop into and out of the quantum field. The QED vacuum of quantum electrodynamics (or QED) was the first vacuum of quantum field theory to be developed. QED originated in the 1930s, and in the late 1940s and early 1950s it was reformulated by Feynman, Tomonaga, and Schwinger, who jointly received the Nobel prize for this work in 1965. For a historical discussion, see fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Roy J
Roy is a masculine given name and a family surname with varied origin. In Anglo-Norman England, the name derived from the Norman ''roy'', meaning "king", while its Old French cognate, ''rey'' or ''roy'' (modern ''roi''), likewise gave rise to Roy as a variant in the Francophone world. In India, Roy is a variant of the surname '' Rai'',. likewise meaning "king".. It also arose independently in Scotland, an anglicisation from the Scottish Gaelic nickname ''ruadh'', meaning "red". Given name * Roy Acuff (1903–1992), American country music singer and fiddler * Roy Andersen (born 1955), runner * Roy Andersen (South Africa) (born 1948), South African businessman and military officer * Roy Anderson (American football) (born 1980), American football coach * Sir Roy M. Anderson (born 1947), British scientific adviser * Roy Andersson (born 1943), Swedish film director * Roy Andersson (footballer) (born 1949), footballer from Sweden * Roy Chapman Andrews (1884–1960), American ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Displacement Operator
In the quantum mechanics study of optical phase space, the displacement operator for one mode is the shift operator in quantum optics, :\hat(\alpha)=\exp \left ( \alpha \hat^\dagger - \alpha^\ast \hat \right ) , where \alpha is the amount of displacement in optical phase space, \alpha^* is the complex conjugate of that displacement, and \hat and \hat^\dagger are the lowering and raising operators, respectively. The name of this operator is derived from its ability to displace a localized state in phase space by a magnitude \alpha. It may also act on the vacuum state by displacing it into a coherent state. Specifically, \hat(\alpha), 0\rangle=, \alpha\rangle where , \alpha\rangle is a coherent state, which is an eigenstate of the annihilation (lowering) operator. Properties The displacement operator is a unitary operator, and therefore obeys \hat(\alpha)\hat^\dagger(\alpha)=\hat^\dagger(\alpha)\hat(\alpha)=\hat, where \hat is the identity operator. Since \hat^\dagger(\alpha)=\ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physical Review
''Physical Review'' is a peer-reviewed scientific journal established in 1893 by Edward Nichols. It publishes original research as well as scientific and literature reviews on all aspects of physics. It is published by the American Physical Society (APS). The journal is in its third series, and is split in several sub-journals each covering a particular field of physics. It has a sister journal, ''Physical Review Letters'', which publishes shorter articles of broader interest. History ''Physical Review'' commenced publication in July 1893, organized by Cornell University professor Edward Nichols and helped by the new president of Cornell, J. Gould Schurman. The journal was managed and edited at Cornell in upstate New York from 1893 to 1913 by Nichols, Ernest Merritt, and Frederick Bedell. The 33 volumes published during this time constitute ''Physical Review Series I''. The American Physical Society (APS), founded in 1899, took over its publication in 1913 and star ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
