On two different kinds of resonances in one-dimensional 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.

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Small-energy series for one-dimensional quantum-mechanical models with non-symmetric potentials

Journal of Mathematical Chemistry ◽

10.1007/s10910-015-0492-8 ◽

2015 ◽

Vol 53 (6) ◽

pp. 1351-1362

Author(s):

Paolo Amore ◽

Francisco M. Fernández

Keyword(s):

Quantum Mechanical ◽

Small Energy ◽

One Dimensional ◽

Mechanical Models

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

Canadian Journal of Physics ◽

10.1139/p96-100 ◽

1996 ◽

Vol 74 (9-10) ◽

pp. 697-700 ◽

Cited By ~ 8

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.

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The role of self-consistency in quantum-mechanical studies of disordered quasi-one-dimensional systems

Chemical Physics ◽

10.1016/0301-0104(84)85154-x ◽

1984 ◽

Vol 86 (1-2) ◽

pp. 41-48 ◽

Cited By ~ 20

Author(s):

B. Gazdy ◽

M. Seel ◽

J. Ladik

Keyword(s):

Quantum Mechanical ◽

One Dimensional ◽

Self Consistency ◽

Mechanical Studies

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Polymer quantum effects on compact stars models

International Journal of Modern Physics D ◽

10.1142/s0218271815500339 ◽

2015 ◽

Vol 24 (05) ◽

pp. 1550033 ◽

Cited By ~ 8

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.

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Contact Electrification by Quantum-Mechanical Tunneling

Research ◽

10.34133/2019/6528689 ◽

2019 ◽

Vol 2019 ◽

pp. 1-11 ◽

Cited By ~ 4

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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