Perturbations into high-order WKB schemes for solving one-dimensional quantum-mechanical models

1995 ◽  
Vol 330 (1-3) ◽  
pp. 49-55 ◽  
Author(s):  
H.P. Gervais ◽  
G. Berthier
Keyword(s):  
High Order ◽  
Quantum Mechanical ◽  
One Dimensional ◽  
Mechanical Models

QUANTIZATION CONDITION FOR HIGHLY EXCITED STATES

1999 ◽  
Vol 14 (19) ◽  
pp. 1237-1242 ◽  
Author(s):  
FRANCISCO M. FERNÁNDEZ ◽  
RAFAEL GUARDIOLA
Keyword(s):  
Perturbation Theory ◽  
Excited States ◽  
Rational Approximation ◽  
Logarithmic Derivative ◽  
Quantization Condition ◽  
Quantum Mechanical ◽  
Anharmonic Oscillators ◽  
One Dimensional ◽  
Simple Quantum ◽  
Mechanical Models

We develop a quantization condition for the excited states of simple quantum-mechanical models. The approach combines perturbation theory for the oscillatory part of the eigenfunction with a rational approximation to the logarithmic derivative of the nodeless part of it. We choose one-dimensional anharmonic oscillators as illustrative examples.

The Riccati–Padé quantization method for one-dimensional quantum-mechanical models

1996 ◽  
Vol 74 (9-10) ◽  
pp. 697-700 ◽  
Author(s):  
Francisco M. Fernández ◽  
R. H. Tipping
Keyword(s):  
Ground State ◽  
Logarithmic Derivative ◽  
Quantum Mechanical ◽  
Quantization Method ◽  
Anharmonic Oscillators ◽  
Eigenvalues And Eigenfunctions ◽  
One Dimensional ◽  
Continuum States ◽  
Separable Models ◽  
Mechanical Models

We improve on a previously developed method for the calculation of accurate eigenvalues and eigenfunctions of separable models in quantum mechanics. It consists of the approximation of the logarithmic derivative of the eigenfunction by means of a rational function or Padé approximant. Here we modify the approach by the separation of the function just mentioned into its odd and even parts, thus making the procedure more efficient for treating asymmetric one-dimensional potentials. We obtain the ground-state eigenvalue of anharmonic oscillators with one and two wells and the lowest resonances of anharmonic oscillators that support only continuum states.

scholarly journals High-order compact LOD methods for solving high-dimensional advection equations

2021 ◽  
Vol 40 (3) ◽  
Author(s):  
Bo Hou ◽  
Yongbin Ge
Keyword(s):  
Truncation Error ◽  
Three Dimensional ◽  
Taylor Series Expansion ◽  
High Order ◽  
High Dimensional ◽  
Analysis Method ◽  
Order Accuracy ◽  
Von Neumann ◽  
One Dimensional ◽  
Von Neumann Analysis

AbstractIn this paper, by using the local one-dimensional (LOD) method, Taylor series expansion and correction for the third derivatives in the truncation error remainder, two high-order compact LOD schemes are established for solving the two- and three- dimensional advection equations, respectively. They have the fourth-order accuracy in both time and space. By the von Neumann analysis method, it shows that the two schemes are unconditionally stable. Besides, the consistency and convergence of them are also proved. Finally, numerical experiments are given to confirm the accuracy and efficiency of the present schemes.

scholarly journals Polymer quantum effects on compact stars models

2015 ◽  
Vol 24 (05) ◽  
pp. 1550033 ◽  
Author(s):  
Guillermo Chacón-Acosta ◽  
Héctor H. Hernandez-Hernandez
Keyword(s):  
Semiclassical Approximation ◽  
Generalized Uncertainty Principle ◽  
Compact Object ◽  
Compact Stars ◽  
One Dimensional ◽  
Degenerate Fermi Gas ◽  
Mechanical Models ◽  
Degeneracy Pressure ◽  
Loop Quantization ◽  
Bose Einstein

In this work we study a completely degenerate Fermi gas at zero temperature by a semiclassical approximation for a Hamiltonian that arises in polymer quantum mechanics. Polymer quantum systems are quantum mechanical models quantized in a similar way as in loop quantum gravity, allowing the study of the discreteness of space and other features of the loop quantization in a simplified way. We obtain the polymer modified thermodynamical properties for this system by noticing that the corresponding Fermi energy is exactly the same as if one directly polymerizes the momentum pF. We also obtain the expansion of the corresponding thermodynamical variables in terms of small values of the polymer length scale λ. We apply these results to study a simple model of a compact one-dimensional star where the gravitational collapse is supported by electron degeneracy pressure. As a consequence, polymer corrections to the mass of the object are found. By using bounds for the polymer length found in Bose–Einstein condensates experiments we compute the modification in the mass of the compact object due to polymer effects of order ~ 10-8. This result is similar to the other order found by different approaches such as generalized uncertainty principle (GUP), and that certainly is within the error reported in typical measurements of white dwarf masses.

scholarly journals Contact Electrification by Quantum-Mechanical Tunneling

Research ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Morten Willatzen ◽  
Zhong Lin Wang
Keyword(s):  
Potential Versus ◽  
Coulomb Repulsion ◽  
Quantum Mechanical ◽  
Quantum Mechanical Tunneling ◽  
One Dimensional ◽  
Contact Electrification ◽  
Order Of Magnitude ◽  
Left And Right ◽  
Tunneling Dynamics ◽  
Vacuum Gap

A simple model of charge transfer by loss-less quantum-mechanical tunneling between two solids is proposed. The model is applicable to electron transport and contact electrification between e.g. a metal and a dielectric solid. Based on a one-dimensional effective-mass Hamiltonian, the tunneling transmission coefficient of electrons through a barrier from one solid to another solid is calculated analytically. The transport rate (current) of electrons is found using the Tsu-Esaki equation and accounting for different Fermi functions of the two solids. We show that the tunneling dynamics is very sensitive to the vacuum potential versus the two solids conduction-band edges and the thickness of the vacuum gap. The relevant time constants for tunneling and contact electrification, relevant for triboelectricity, can vary over several orders of magnitude when the vacuum gap changes by one order of magnitude, say, 1 Å to 10 Å. Coulomb repulsion between electrons on the left and right material surfaces is accounted for in the tunneling dynamics.

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