Schrodinger equation scattering

Balint-Kurti G G, Dixon R N and Marston C C 1992 Grid methods for solving the Schrodinger equation and time-dependent quantum dynamics of molecular photofragmentation and reactive scattering processes/of. Rev. Phys. Chem. 11 317—44... 

We use s, p, and d partial waves, 16 energy points on a semi circular contour, 135 special k-points in the l/12th section of the 2D Brillouin zone and 13 plane waves for the inter-layer scattering. The atomic wave functions were determined from the scalar relativistic Schrodinger equation, as described by D. D. Koelling and B. N. Harmon in J. Phys. C 10, 3107 (1977). 

Raman scattering Schrodinger equation 138, 262 SCS see centrifugal sudden (CS) approximation... 

Tsoucaris, decided to treat by Fourier transformation, not the Schrodinger equation itself, but one of its most popular approximate forms for electron systems, namely the Hartree-Fock equations. The form of these equations was known before, in connection with electron-scattering problems [13], but their advantage for Quantum Chemistry calculations was not yet recognized. 

PES), which is different for each electronic state of the system (i.e. each eigenfunction of the BO Schrodinger equation). Based on these PESs, the nuclear Schrodinger equation is solved to define, for example, the possible nuclear vibrational levels. This approach will be used below in the description of the nuclear inelastic scattering (NIS) method. 

Discrete Fourier transform (DFT), non-adiabatic coupling, Longuet-Higgins phase-based treatment, two-dimensional two-surface system, scattering calculation, 153-155 Discrete variable representation (DVR) direct molecular dynamics, nuclear motion Schrodinger equation, 364-373 non-adiabatic coupling, quantum dressed classical mechanics, 177-183 formulation, 181-183... 

The typical way to open a billiard is to attach some reservoirs with continuous energy spectrum, for example, the leads or microwave waveguides, as shown in fig. 3 below. Full information about the scattering properties of the billiard is given by the scattering wave function which is a solution of the Schrodinger equation Hip = Exp with the total Hamiltonian... 

Schrodinger Equation with Absorbing Potential for Quantum Scattering Calculations. 

The simplest form of scattering theory is for a single particle moving in a local external potential. If we ignore relativistic effects and return to the Schrodinger equation... 

The quantum theory of molecular collisions in external fields described in this chapter is based on the solutions of the time-independent Schrodinger equation. The scattering formalism considered here can be used to calculate the collision properties of molecules in the presence of static electric or magnetic fields as well as in nonresonant AC fields. In the latter case, the time-dependent problem can be reduced to the time-independent one by means of the Floquet theory, discussed in the previous section. We will consider elastic or inelastic but chemically nonreac-tive collisions of molecules in an external field. The extension of the formalism to reactive scattering problems for molecules in external fields has been described in Ref. [12]. 

A central problem in physics and chemistry has always been the solution of the Schrodinger equation (SE) for stationary states. Such stationary states may relate to electronic structure problems, in which case one is primarily interested in bound states, or to scattering problems, in which case the stationary solutions are continuum states. In both cases, one of the most powerful tools in the theoretical arsenal for solving such problems is the partitioning technique (PT), which has been developed in a series of papers prominently by Per-Olov Lowdin [1-6] and Herman Feshbach [7-9]. 

Numerical integration of the radial Schrodinger equation is generally necessary if realistic interaction potentials are selected. For this purpose, efficient computer codes exist based, for example, on Cooley s method of integration. Other widely available codes written to compute scattering... 

Suppose they approach each other, interact, then move away. This scattering process is described by a joint Schrodinger equation for lP(ql, q2, t) with initial condition (1.17). The point is that after the interaction has taken place the wave function (4i,42,0 no longer factorizes as in (1.17). The separated molecules cannot be described by separate wave functions, but only by the joint wave function, or else by their density matrices pj and p2. This is considered a paradox by those who have not learned to live with quantum mechanics. ... 

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