Coherent states in mathematical physics

About: Coherent states in mathematical physics is a research topic. Over the lifetime, 732 publications have been published within this topic receiving 32024 citations.

Application of the Fock Expansion to Doubly Excited States of the Helium Atom

Abstract: The formal properties of the Fock expansion of helium-atom wave functions provide a frame within which the behavior of doubly excited $^{1}P$ states can be simply expressed. The convergence of the expansion is investigated.

Quantization, coherent states, and complex structures

Abstract: Quantization, Field Theory, and Representation Theory: On Quantum Mechanics in a Curved Spacetime with Absolute Time (D. Canarutto et al.). Massless Spinning Particles on the Antide Sitter Spacetime (S. De Bievre, S. Mehdi). A Family of Nonlinear Schroedinger Equations: Linearizing Transformations and Resulting Structure (H.D. Doebner et al.). Modular Structures in Geometric Quantization (G.G. Emch). Diffeomorphism Groups and Anyon Fields (G.A. Goldin, D.H. Sharp). On a Full Quanization of the Torus (M.J. Gotay). Differential Forms on the Skyrmion Bundle (C. Gross). Explicitly Covariant Algebraic Representations for Transitional Currents of Spin1/2 Particles (M.I. Krivoruchenko). The Quantum Su(2,2)Harmonic Oscillator (W. Mulak). GeometricStochastic Quantization and Quantum Geometry (E. Prugovecki). Prequantization (D.J. Simms). Classical Yang-Mills and Dirac Fields in the Minkowski Space and in a Bag (J. Sniatycki). Symplectic Induction, Unitary Induction and BRST Theory (Summary) (G.M. Tuynman). Coherent States, Complex and Poisson Structures: Spin Coherent States for the Poincare Group (S.T. Ali, J.P. Gazeau). Coherent States and Global Differential Geometry (S. Berceanu). Natural Transformations of Lagrangians into pforms on the Tangent Bundle (J. Debecki). SL(2,IR)Coherent States and Itegrable Systems in Classical and Quantum Physics (J.P. Gazeau). Symplectic and Lagrangian Realization of Poisson Manifolds (M. Giordano et al.). From the Poincare-Cartan Form to a Gerstehhaber Algebra of Poisson Brackets in Field Theory (I.V. Kanatchikov). Geometric Coherent States, Membranes, and Star Products (M. Karasev). Integral Representation of Eigenfunctions and Coherent States for the Zeeman Effect (M. Karasev, E. Novikova). QDeformations and Quantum Groups, Noncommutative Geometry: Quantum Coherent States and the Method of Orbits (B. Jurco, P. tovicek). On the Deformation of Commutation Relations (W. Marcinek). The qdeformed Quantum Mechanics in the Coherent States Map Approach (V. Maximov, A. Odzijewicz). Quantization by Quadratic Polynomials in Creation and Annihilation Operators (W. Slowikowski). On Dirac Type Brackets (Yu.M. Vorobjev, R. Flores Espinoza). Quantum Trigonometry and Phasespace Propensity (K. Wodkiewicz, B.G. Englert). Noncommutative Space-Time Impled by Spin (S. Zadrzewski). Miscellaneous Problems of Quantum Dynamics: Spectrum of the Dirac Operator on the SU(2) Manifold as Energy Spectrum for the Polyaniline Macromolecule (H. Makaruk). On Geometric Methods in the Description of Quantum Fluids (R. Owczarek). Galactic Dynamics in the Siegel Halfplane (G. Rosensteel). Graded Contractions of so(4,2) (J. Tolar, P. Travnicek). The Berry Phase and the Geometry of Coset Spaces (E.A. Tolkachev, A.A. Tregubovich). Index.

Exactly solvable `discrete' quantum mechanics; shape invariance, Heisenberg solutions, annihilation-creation operators and coherent states

Abstract: Various examples of exactly solvable `discrete' quantum mechanics are explored explicitly with emphasis on shape invariance, Heisenberg operator solutions, annihilation-creation operators, the dynamical symmetry algebras and coherent states. The eigenfunctions are the (q-)Askey-scheme of hypergeometric orthogonal polynomials satisfying difference equation versions of the Schr\"odinger equation. Various reductions (restrictions) of the symmetry algebra of the Askey-Wilson system are explored in detail.

The q-deformed harmonic oscillator, coherent states, and the uncertainty relation

Abstract: For a q-deformed harmonic oscillator, we find explicit coordinate representations of the creation and annihilation operators, eigenfunctions, and coherent states (the last being defined as eigenstates of the annihilation operator). We calculate the product of the “coordinate-momentum” uncertainties in q-oscillator eigenstates and in coherent states. For the oscillator, this product is minimum in the ground state and equals 1/2, as in the standard quantum mechanics. For coherent states, the q-deformation results in a violation of the standard uncertainty relation; the product of the coordinate-and momentum-operator uncertainties is always less than 1/2. States with the minimum uncertainty, which tends to zero, correspond to the values of λ near the convergence radius of the q-exponential.