Semiclassical Nonadiabatic Surface-hopping Wave Function Expansion at Low Energies: Hops in the Forbidden Region†

2008 ◽  
Vol 112 (50) ◽  
pp. 15966-15972 ◽  
Author(s):  
Michael F. Herman
Keyword(s):  
Wave Function ◽  
Surface Hopping ◽  
Function Expansion ◽  
Low Energies ◽  
Forbidden Region

scholarly journals Homogeneous Field and WKB Approximation in Deformed Quantum Mechanics with Minimal Length

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
Jun Tao ◽  
Peng Wang ◽  
Haitang Yang
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Statistical Physics ◽  
Turning Point ◽  
Minimal Length ◽  
Jacobi Method ◽  
Homogeneous Field ◽  
Quantization Rule ◽  
Connection Formula ◽  
Forbidden Region

In the framework of the deformed quantum mechanics with a minimal length, we consider the motion of a nonrelativistic particle in a homogeneous external field. We find the integral representation for the physically acceptable wave function in the position representation. Using the method of steepest descent, we obtain the asymptotic expansions of the wave function at large positive and negative arguments. We then employ the leading asymptotic expressions to derive the WKB connection formula, which proceeds from classically forbidden region to classically allowed one through a turning point. By the WKB connection formula, we prove the Bohr-Sommerfeld quantization rule up toOβ2. We also show that if the slope of the potential at a turning point is too steep, the WKB connection formula is no longer valid around the turning point. The effects of the minimal length on the classical motions are investigated using the Hamilton-Jacobi method. We also use the Bohr-Sommerfeld quantization to study statistical physics in deformed spaces with the minimal length.

scholarly journals Nonadiabatic dynamics in multidimensional complex potential energy surfaces

2020 ◽  
Vol 11 (36) ◽  
pp. 9827-9835 ◽  
Author(s):  
Fábris Kossoski ◽  
Mario Barbatti
Keyword(s):  
Wave Function ◽  
Potential Energy ◽  
Complex Potential ◽  
Potential Energy Surfaces ◽  
Nonadiabatic Dynamics ◽  
Continuous Development ◽  
Surface Hopping ◽  
Multidimensional Complex ◽  
Function Norm ◽  
Energy Surfaces

Despite the continuous development of methods for describing nonadiabatic dynamics, there is a lack of multidimensional approaches for processes where the wave function norm is not conserved. A new surface hopping variant closes this knowledge gap.

Scattering by Two Impenetrable Spheres

1973 ◽  
Vol 51 (17) ◽  
pp. 1850-1860
Author(s):  
M. Razavy
Keyword(s):  
Wave Function ◽  
Scattering Amplitude ◽  
Hard Spheres ◽  
Scattering Length ◽  
Separation Of Variables ◽  
Scattered Wave ◽  
Simple Expression ◽  
Rigid Spheres ◽  
Low Energies ◽  
Bispherical Coordinates

The problem of multiple scattering by two rigid spheres is studied in the context of an effective range theory. At low energies, by expanding the total wave function in powers of the momentum of the incident particle, it is observed that the coefficients of different terms of the expansion are solutions of either Laplace or Poisson equations. These equations are separable in bispherical coordinates. Using the method of separation of variables, one can determine the scattering amplitude and its first and second derivatives with respect to momentum, at zero energy. In particular, a simple expression is obtained for the scattering length of two hard spheres. With the help of the Green's function in bispherical coordinates, it is shown that for any wavenumber, the scattered wave satisfies an inhomogeneous integral equation in two variables. Hence, the exact wave function and the scattering amplitude can be found numerically for all energies.

scholarly journals Surface Motion of a Half-Space Containing an Elliptical-Arc Canyon under Incident SH Waves

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1884
Author(s):  
Hui Qi ◽  
Fuqing Chu ◽  
Jing Guo ◽  
Runjie Yang
Keyword(s):  
Wave Function ◽  
Half Space ◽  
Wave Scattering ◽  
Scattering Problem ◽  
Expansion Method ◽  
Numerical Results ◽  
Mathieu Function ◽  
Axis Ratio ◽  
Function Expansion ◽  
Wave Function Expansion Method

The existence of local terrain has a great influence on the scattering and diffraction of seismic waves. The wave function expansion method is a commonly used method for studying terrain effects, because it can reveal the physical process of wave scattering and verify the accuracy of numerical methods. An exact, analytical solution of two-dimensional scattering of plane SH (shear-horizontal) waves by an elliptical-arc canyon on the surface of the elastic half-space is proposed by using the wave function expansion method. The problem of transforming wave functions in multi-ellipse coordinate systems was solved by using the extra-domain Mathieu function addition theorem, and the steady-state solution of the SH wave scattering problem of elliptical-arc depression terrain was reduced to the solution of simple infinite algebra equations. The numerical results of the solution are obtained by truncating the infinite equation. The accuracy of the proposed solution is verified by comparing the results obtained when the elliptical arc-shaped depression is degraded into a semi-ellipsoidal depression or even a semi-circular depression with previous results. Complicated effects of the canyon depth-to-span ratio, elliptical axis ratio, and incident angle on ground motion are shown by the numerical results for typical cases.

Globally uniform semiclassical surface-hopping wave function for nonadiabatic scattering

2004 ◽  
Vol 120 (16) ◽  
pp. 7383-7390 ◽  
Author(s):  
Michael F. Herman ◽  
Ouafae El Akramine ◽  
Michael P. Moody
Keyword(s):  
Wave Function ◽  
Surface Hopping
Sign in / Sign up

Export Citation Format

Share Document