Calculation of Matrix Elements for One‐Dimensional Quantum‐Mechanical Problems

1968 ◽  
Vol 49 (9) ◽  
pp. 4209-4211 ◽  
Author(s):  
A. S. Dickinson ◽  
P. R. Certain
Keyword(s):  
Quantum Mechanical ◽  
Matrix Elements ◽  
One Dimensional

SYMMETRY DECOUPLING IN LINEAR ALGEBRAIC VARIATIONAL SCATTERING PROBLEMS

1995 ◽  
Vol 06 (01) ◽  
pp. 105-121
Author(s):  
MEISHAN ZHAO
Keyword(s):  
Angular Momentum ◽  
Variational Principle ◽  
Total Angular Momentum ◽  
Numerical Calculations ◽  
Quantum Mechanical ◽  
Matrix Elements ◽  
Scattering Problems ◽  
Identical Particles ◽  
Generalized Newton

This paper discusses the symmetry decoupling in quantum mechanical algebraic variational scattering calculations by the generalized Newton variational principle. Symmetry decoupling for collisions involving identical particles is briefly discussed. Detailed discussion is given to decoupling from evaluation of matrix elements with nonzero total angular momentum. Example numerical calculations are presented for BrH2 and DH2 systems to illustrate accuracy and efficiency.

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.

Efficient computation of one-electron two-centre exchange integrals in ion–atom collisions

1976 ◽  
Vol 54 (9) ◽  
pp. 944-949 ◽  
Author(s):  
Alfred Msezane
Keyword(s):  
Principal Quantum Number ◽  
Computing Time ◽  
Translational Motion ◽  
Matrix Elements ◽  
Efficient Computation ◽  
Close Coupling ◽  
One Dimensional ◽  
State Approximation ◽  
The Matrix ◽  
Exchange Matrix

A scheme is presented for the reduction to one-dimensional integrals of any one-electron two-centre exchange matrix elements which incorporate the momentum associated with the translational motion of the electron. These elements are of the types occurring in close coupling-based treatments of ion–atom collisions. It is shown in a six state approximation, by coupling both eigenstates and pseudostates for the asymmetric He2+–H collision process, that computing time for the evaluation of the matrix elements is determined mainly by the number of different exponents in the matrix elements. The coupling of additional states with the same principal quantum number as the already coupled ones alters computing time insignificantly.

scholarly journals One-loop non-planar anomalous dimensions in super Yang-Mills theory

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Tristan McLoughlin ◽  
Raul Pereira ◽  
Anne Spiering
Keyword(s):  
Perturbation Theory ◽  
Integrable Systems ◽  
Chaotic Systems ◽  
Quantum Mechanical ◽  
Matrix Elements ◽  
Mechanical Perturbation ◽  
Yang Mills ◽  
Anomalous Dimensions ◽  
Dilatation Operator ◽  
Scalar Products

Abstract We consider non-planar one-loop anomalous dimensions in maximally supersymmetric Yang-Mills theory and its marginally deformed analogues. Using the basis of Bethe states, we compute matrix elements of the dilatation operator and find compact expressions in terms of off-shell scalar products and hexagon-like functions. We then use non-degenerate quantum-mechanical perturbation theory to compute the leading 1/N2 corrections to operator dimensions and as an example compute the large R-charge limit for two-excitation states through subleading order in the R-charge. Finally, we numerically study the distribution of level spacings for these theories and show that they transition from the Poisson distribution for integrable systems at infinite N to the GOE Wigner-Dyson distribution for quantum chaotic systems at finite N.

A study of the ‘irreversibility paradox’ for a simple statistical assembly

1956 ◽  
Vol 52 (4) ◽  
pp. 712-718 ◽  
Author(s):  
H. N. V. Temperley
Keyword(s):  
Simple Model ◽  
Second Step ◽  
Quantum Mechanical ◽  
Diffusion Type ◽  
One Dimensional ◽  
The Third ◽  
Mechanical Description ◽  
Quantum Mechanical Description

ABSTRACTA very simple model, consisting of N particles moving in a one-dimensional assembly divided by potential ‘humps’ into M cells, is studied. The process of passing from a quantum-mechanical description of such an assembly to the equation of diffusion type that governs it in practice is shown to consist of at least three separate steps: ‘averaging over phases’, and letting N and M become large. The effects of these steps are considered separately. Strict irreversibility in time appears after the first step, but the assembly remains ergodic until after the second step and fluctuations persist until after the third step.

Collective motion in the nuclear shell model III. The calculation of spectra

1963 ◽  
Vol 272 (1351) ◽  
pp. 557-577 ◽  
Keyword(s):  
Shell Model ◽  
Collective Motion ◽  
Mass Region ◽  
Wave Functions ◽  
Nuclear Shell Model ◽  
Matrix Elements ◽  
One Dimensional ◽  
The One ◽  
Nuclear Shell ◽  
Main Pattern

A method is derived for calculating matrix elements of a two-body interaction in wave functions which were classified in part I interms of the group U 2- . For simplicity, a Cartesian basis of intrinsic functions is introduced in which the one-dimensional oscillators in x, y and z are separately diagonal. An application to 24 Mg in L-S coupling shows very little mixing of the quantum number K but an appreciable (10 to 20 %) mixing of U 3 representations (λμ). Overall agreement with experiment is quantitatively only tolerable but the main pattern of the spectrum is undoubtedly given by the lowest representation (84). On this basis, suggestions are made concerning the type of spectra to be expected for even and odd parity levels of the even-even nuclei in the mass region 16 < A < 40.

Matrix Elements of One Dimensional Explicitly Correlated Gaussian Basis Functions

2019 ◽  
Vol 61 (1) ◽  
Author(s):  
Timothy Zaklama ◽  
David Zhang ◽  
Keefer Rowan ◽  
Louis Schatzki ◽  
Yasuyuki Suzuki ◽  
...  
Keyword(s):  
Basis Functions ◽  
Matrix Elements ◽  
One Dimensional ◽  
Explicitly Correlated ◽  
Gaussian Basis Functions
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