A new approach to the computational solution of the Schfbdinger equation is based on the partial transformation of the Hamiltonian to a tridiagonal matrix. The method is especially suited to tight-binding Hamiltonians encountered in solid state physics and permits of the order of iodegrees of freedo
Recursive solution of Liouville's equation
β Scribed by Roger Haydock; David B. Kim
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 745 KB
- Volume
- 87
- Category
- Article
- ISSN
- 0010-4655
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π SIMILAR VOLUMES
dq N dp N Ο const, (3a) A numerical method for the time evolution of systems described by Liouville-type equations is derived. The algorithm uses a lattice of numerical markers, which follow exactly Hamiltonian trajectories, to represent the operator d/dt in moving (i.e., Lagrangian) coordinates. H
We consider an equation &y"(x)+q(x) y(x)=f (x), x # R; ( 1 ) We study requirements for a weight function r(x) # L loc p (R) and for q(x) under which, for a given p # [1, ], regardless of f (x) # L p (R), the solution y(x) # L p (R) of Eq. (1) satisfies the inequalities: