Topic

# WKB approximation

About: WKB approximation is a research topic. Over the lifetime, 5173 publications have been published within this topic receiving 98734 citations. The topic is also known as: WKB method.

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01 Jan 1971

TL;DR: In this paper, one-body problems without spin are discussed. And the Wentzel-Kramers Brillouin (WKB) approximation of the WKB is used.

Abstract: Part I: One-Body Problems without Spin. One-Dimensional Problems. Problems of Two or Three Degrees of Freedom without Spherical Symmetry. The Angular Momentum. Potentials of Spherical Symmetry. The Wentzel-Kramers Brillouin (WKB) Approximation. The Magnetic Field.- Part II: Particles with Spin. One-Body Problems. Two-and Three-Body Problems. Many-Body Problems. Few Particles. Very Many Particles: Quantum Statistics. Non-Stationary Problems. The Relativistic Dirac Equation. Radiation Theory. Mathematical Appendix.

2,190 citations

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01 Jan 2001

TL;DR: In this paper, the Wigner Function was used to determine the square root of a Delta Function and Bessel Functions were used to calculate the Moyal Function of a Harmonic Oscillator.

Abstract: What is Quantum Optics? Ante The Wigner Function Quantum States in Phase Space Waves a la WKB WKB Wave Functions and Berry's Phase Interference in Phase Space Applications of Interference in Phase Space Wave Packet Dynamics Quantization of the Radiation Field Quantum States of the Radiation Field Phase Space Functions Optical Interferometry Atom-Field Interaction Dynamics of Jaynes-Cummings-Paul Model State Preparation and Entanglement The Paul Trap Damping and Amplification Atom Optics in Quantized Light Fields Wigner Functions in Atom Optics Appendix Time Dependent Operators - Derivation of Equations Determining the Moyal Function - Energy Wave Functions of Harmonic Oscillator - Method of Stationary Phase - Radial Equation - Airy Function - Asymptotic Expansion of the Poisson Distribution - Area of Overlap - P-Distributions - Homodyne Detection Kernel - Effective Hamiltonian - Spontaneous Emission - A Model for the Square Root of a Delta Function - Bessel Functions

1,420 citations

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TL;DR: In this paper, the first baroclinic gravity-wave phase speed c1 and the Rossby radius of deformation l1 are computed from climatological average temperature and salinity profiles.

Abstract: Global 1 83 18 climatologies of the first baroclinic gravity-wave phase speed c1 and the Rossby radius of deformation l1 are computed from climatological average temperature and salinity profiles. These new atlases are compared with previously published 5 83 58 coarse resolution maps of l1 for the Northern Hemisphere and the South Atlantic and with a 1 83 18 fine-resolution map of c1 for the tropical Pacific. It is concluded that the methods used in these earlier estimates yield values that are biased systematically low by 5%‐15% owing to seemingly minor computational errors. Geographical variations in the new high-resolution maps of c1 and l1 are discussed in terms of a WKB approximation that elucidates the effects of earth rotation, stratification, and water depth on these quantities. It is shown that the effects of temporal variations of the stratification can be neglected in the estimation of c1 and l1 at any particular location in the World Ocean. This is rationalized from consideration of the WKB approximation.

1,137 citations

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TL;DR: In this article, a review of various methods of deriving expressions for quantum-mechanical quantities in the limit when hslash is small (in comparison with the relevant classical action functions) is presented.

Abstract: We review various methods of deriving expressions for quantum-mechanical quantities in the limit when hslash is small (in comparison with the relevant classical action functions). To start with we treat one-dimensional problems and discuss the derivation of WKB connection formulae (and their reversibility), reflection coefficients, phase shifts, bound state criteria and resonance formulae, employing first the complex method in which the classical turning points are avoided, and secondly the method of comparison equations with the aid of which uniform approximations are derived, which are valid right through the turningpoint regions. The special problems associated with radial equations are also considered. Next we examine semiclassical potential scattering, both for its own sake and also as an example of the three-stage approximation method which must generally be employed when dealing with eigenfunction expansions under semiclassical conditions, when they converge very slowly. Finally, we discuss the derivation of semiclassical expressions for Green functions and energy level densities in very general cases, employing Feynman's path-integral technique and emphasizing the limitations of the results obtained. Throughout the article we stress the fact that all the expressions obtained involve quantities characterizing the families of orbits in the corresponding purely classical problems, while the analytic forms of the quantal expressions depend on the topological properties of these families. This review was completed in February 1972.

1,068 citations

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TL;DR: In this article, a new formulation of an approximate conservation relation of wave-activity pseudomentum is derived, which is applicable for either stationary or migratory quasigeostrophic (QG) eddies on a zonally varying basic flow.

Abstract: A new formulation of an approximate conservation relation of wave-activity pseudomomentum is derived, which is applicable for either stationary or migratory quasigeostrophic (QG) eddies on a zonally varying basic flow. The authors utilize a combination of a quantity A that is proportional to wave enstrophy and another quantity E that is proportional to wave energy. Both A and E are approximately related to the wave-activity pseudomomentum. It is shown for QG eddies on a slowly varying, unforced nonzonal flow that a particular linear combination of A and E, namely, M ≡ (A + E)/2, is independent of the wave phase, even if unaveraged, in the limit of a small-amplitude plane wave. In the same limit, a flux of M is also free from an oscillatory component on a scale of one-half wavelength even without any averaging. It is shown that M is conserved under steady, unforced, and nondissipative conditions and the flux of M is parallel to the local three-dimensional group velocity in the WKB limit. The autho...

978 citations