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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 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 disp .... 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.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. ... [...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 that 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 relat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eigenstates
In quantum physics, a quantum state is a mathematical entity that embodies the knowledge of a quantum system. Quantum mechanics specifies the construction, evolution, and measurement of a quantum state. The result is a prediction for the system represented by the state. Knowledge of the quantum state, and the rules for the system's evolution in time, exhausts all that can be known about a quantum system. Quantum states may be defined differently for different kinds of systems or problems. Two broad categories are * wave functions describing quantum systems using position or momentum variables and * the more abstract vector quantum states. Historical, educational, and application-focused problems typically feature wave functions; modern professional physics uses the abstract vector states. In both categories, quantum states divide into pure versus mixed states, or into coherent states and incoherent states. Categories with special properties include stationary states for time i ... [...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 creation operator i ... [...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. However, the quantum vacuum is not a simple empty space, 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 for example For the Nobel prize details and the Nobel lectures by these authors, see Today, the electromagnetic interactions and the weak interactions are unified (at very high energies only) in the theory of the electroweak interaction. The Standard Model is a generalization ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Roy J
Roy or Roi is a masculine given name and a family surname with varied origins. France In France, this family name originated from the Normans, the descendants of Norse Vikings who migrated to Amigny, a commune in Manche, Normandy.. The derivation is from the Old French ''roy'', ''roi'' (), meaning "king", which was a Epithet">byname used before the Norman Conquest and a personal name in the Middle Ages">Norman_Conquest.html" ;"title="Epithet">byname used before the Norman Conquest">Epithet">byname used before the Norman Conquest and a personal name in the Middle Ages. Earliest references cite ''Guillaume de Roy'' (William of Roy), who was a knight of the Knights Templar and one of several knights and feudal lords (seigneur) of the Roy family in France and Switzerland. In Canada and in the United States, the descendants of the families of Roy, Le Roy that immigrated to North America have been granted a coat of arms by the Governor General of Canada. England After the N ... [...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. This operator was introduced independently by Richard Feynman and Roy J. Glauber in 1951. Properties The displacement operator is a unitary operator, and therefore obeys \hat(\alpha)\hat^\dagger(\alpha)=\hat^\dagger( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physical Review
''Physical Review'' is a peer-reviewed scientific journal. The journal was 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 publicati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
