scholarly journals WKB and “cubic-WKB” methods as an adiabatic approximation

2019 ◽  
Vol 34 (31) ◽  
pp. 1950250
Author(s):  
Shinji Iida
Keyword(s):  
Wave Function ◽  
Adiabatic Approximation ◽  
Order Correction ◽  
Approximation Schemes ◽  
Wkb Method ◽  
Adiabatic Expansion ◽  
Divergence Problem

This paper shows that WKB wave function can be expressed in the form of an adiabatic expansion. To build a bridge between two widely invoked approximation schemes seems pedagogically instructive. Further, “cubic-WKB” method that has been devised in order to overcome the divergence problem of WKB can be also presented in the form of an adiabatic approximation: The adiabatic expansion of a wave function contains a certain parameter. When this parameter is adjusted so as to make the next order correction vanish approximately, the adiabatic wave function becomes equivalent to that of the “cubic-WKB”.

scholarly journals Electronic non-adiabatic states: towards a density functional theory beyond the Born–Oppenheimer approximation

2014 ◽  
Vol 372 (2011) ◽  
pp. 20130059 ◽  
Author(s):  
Nikitas I. Gidopoulos ◽  
E. K. U. Gross
Keyword(s):  
Wave Function ◽  
Density Functional ◽  
Adiabatic Approximation ◽  
Complete System ◽  
Wave Functions ◽  
Nuclear Wave Function ◽  
Functional Theory ◽  
Novel Treatment ◽  
Oppenheimer Approximation ◽  
Adiabatic Case

A novel treatment of non-adiabatic couplings is proposed. The derivation is based on a theorem by Hunter stating that the wave function of the complete system of electrons and nuclei can be written, without approximation, as a Born–Oppenheimer (BO)-type product of a nuclear wave function, X ( R ), and an electronic one, Φ R ( r ), which depends parametrically on the nuclear configuration R . From the variational principle, we deduce formally exact equations for Φ R ( r ) and X ( R ). The algebraic structure of the exact nuclear equation coincides with the corresponding one in the adiabatic approximation. The electronic equation, however, contains terms not appearing in the adiabatic case, which couple the electronic and the nuclear wave functions and account for the electron–nuclear correlation beyond the BO level. It is proposed that these terms can be incorporated using an optimized local effective potential.

NON-ADIABATIC COUPLED REARRANGEMENT CHANNEL CALCULATION OF ENERGY FOR MUONIC MOLECULE ttμ IN THE HYPER-SPHERICAL APPROACH

2006 ◽  
Vol 15 (01) ◽  
pp. 247-254
Author(s):  
M. MAHDAVI
Keyword(s):  
Binding Energy ◽  
Ground State ◽  
Bound States ◽  
Adiabatic Approximation ◽  
Spherical Surface ◽  
Molecular Ions ◽  
Adiabatic Expansion ◽  
Muonic Molecule ◽  
Channel Calculation ◽  
Three Body

The hyper-spherical adiabatic expansion is a representation for the investigation of the muonic three-body bound states. In this research, we have used the method of hyper-spherical "surface" functions for the muonic molecule, tritium-tritium-muon. Through this approach, the binding energy of the ground state and the lowest eigenpotentials for the muonic molecular ions are calculated in the extreme adiabatic approximation. The results obtained are close to the calculation of other researchers.

scholarly journals SCATTERING OF SCALAR FIELD BY AN EXTENDED BLACK HOLE IN F(R) GRAVITY

2014 ◽  
Vol 29 (02) ◽  
pp. 1450005 ◽  
Author(s):  
SANEESH SEBASTIAN ◽  
V. C. KURIAKOSE
Keyword(s):  
Black Hole ◽  
Wave Function ◽  
Scalar Field ◽  
Cross Section ◽  
Absorption Cross Section ◽  
Hawking Temperature ◽  
Wkb Method ◽  
Absorption Cross ◽  
Tunneling Method

In this work we have studied the scattering of scalar field around an extended black hole in F(R) gravity using WKB method. We have obtained the wave function in different regions such as near the horizon region, away from horizon and far away from horizon and the absorption cross-section are calculated. We find that the absorption cross-section is inversely proportional to the cube of Hawking temperature. We have also evaluated the Hawking temperature of the black hole via tunneling method.

CALCULATION OF BINDING ENERGY FOR THE CHARGE-NONSYMMETRIC MUONIC MOLECULES IN THE HYPER-SPHERICAL APPROACH

2005 ◽  
Vol 20 (02) ◽  
pp. 145-153 ◽  
Author(s):  
M. R. ESKANDARI ◽  
M. MAHDAVI
Keyword(s):  
Binding Energy ◽  
Ground State ◽  
Bound States ◽  
Adiabatic Approximation ◽  
Spherical Surface ◽  
Molecular Ions ◽  
Adiabatic Expansion ◽  
Three Body

The hyper-spherical adiabatic expansion is a representation for the investigation of the muonic three-body bound states. In this research we have used the method of hyper-spherical "surface" functions for charge-nonsymmetric muonic molecules (isotopes of helium-deuterium-muon). Through this approach, the binding energy of the ground state and the lowest eigenpotentials for the muonic molecular ions are calculated in extreme adiabatic approximation. The obtained results are close to other's calculation.

scholarly journals ALPHA-PARTICLE MOMENTUM DISTRIBUTIONS FROM 12C DECAYING RESONANCES

2008 ◽  
Vol 17 (10) ◽  
pp. 2188-2193 ◽  
Author(s):  
R. ÁLVAREZ-RODRÍGUEZ ◽  
A. S. JENSEN ◽  
D. V. FEDOROV ◽  
H. O. U. FYNBO ◽  
E. GARRIDO
Keyword(s):  
Wave Function ◽  
Alpha Particle ◽  
Expansion Method ◽  
Wave Functions ◽  
Angular Distributions ◽  
Adiabatic Expansion ◽  
Energy Distributions ◽  
Momentum Distributions ◽  
Particle Momentum ◽  
Hyperspherical Adiabatic

The computed α particle momentum distributions from the decay of low-lying 12 C resonances are shown. The wave function of the decaying fragments is computed by means of the complex scaled hyperspherical adiabatic expansion method. The large-distance part of the wave functions is crucial and has to be accurately calculated. We discuss energy distributions, angular distributions and Dalitz plots for the 4+, 1+ and 4- states of 12 C .

scholarly journals ASYMPTOTICALLY VANISHING COSMOLOGICAL CONSTANT IN THE MULTIVERSE

2011 ◽  
Vol 26 (18) ◽  
pp. 3107-3120 ◽  
Author(s):  
HIKARU KAWAI ◽  
TAKASHI OKADA
Keyword(s):  
Wave Function ◽  
Partition Function ◽  
Cosmological Constant ◽  
Space Time ◽  
The Other ◽  
Wkb Method ◽  
Leading Order ◽  
Lorentzian Space ◽  
Euclidean Wormholes ◽  
The Universe

We study the problem of the cosmological constant in the context of the multiverse in Lorentzian space–time, and show that the cosmological constant will vanish in the future. This sort of argument was started by Sidney Coleman in 1989, and he argued that the Euclidean wormholes make the multiverse partition function a superposition of various values of the cosmological constant Λ, which has a sharp peak at Λ = 0. However, the implication of the Euclidean analysis to our Lorentzian space–time is unclear. With this motivation, we analyze the quantum state of the multiverse in Lorentzian space–time by the WKB method, and calculate the density matrix of our universe by tracing out the other universes. Our result predicts vanishing cosmological constant. While Coleman obtained the enhancement at Λ = 0 through the action itself, in our Lorentzian analysis the similar enhancement arises from the front factor of eiS in the universe wave function, which is in the next leading order in the WKB approximation.

scholarly journals NON-ADIABATIC ARBITRARY GEOMETRIC PHASE GATE IN 2-QUBIT SPIN MODEL

2007 ◽  
Vol 21 (15) ◽  
pp. 909-921
Author(s):  
YU TONG
Keyword(s):  
Wave Function ◽  
Geometric Phase ◽  
Adiabatic Approximation ◽  
Spin Model ◽  
Time Dependent ◽  
Magnetic Pulse ◽  
Harmonic Frequency ◽  
Time Duration ◽  
Quantum Phase Gate ◽  
Phase Gate

We study a 2-qubit spin model for the possibility of realizing an arbitrary geometric quantum phase gate in terms of a single coherent magnetic pulse with multi-harmonic frequency. Using resonant transition approximation, the time-dependent Hamiltonian of two coupled spins can be solved analytically. The time evolution of the wave function is obtained without adiabatic approximation. The parameters of magnetic pulse, such as the frequency, amplitude, phase of each harmonic part as well as the time duration of the pulse are determined for achieving an arbitrary non-adiabatic geometric phase gate. The requirement of materials for realizing such a gate is analyzed. As a result, the non-adiabatic geometric controlled phase gates and A–A phase are also addressed.

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