Invariant domains for the time-dependent Schrödinger equation
✍ Scribed by Charles Radin; Barry Simon
- Publisher
- Elsevier Science
- Year
- 1978
- Tongue
- English
- Weight
- 381 KB
- Volume
- 29
- Category
- Article
- ISSN
- 0022-0396
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## Abstract In this paper we study local and global well‐posedness in __L__^2^ and __H__^1^ of the Cauchy problem for the following nonlinear Schrödinger equations equation image in the space ℝ^1+__n__^ , with __n__ ≥ 2. The coefficient __a__ (__t__) is assumed to be positive, and possibly vanish
We present several new finite-difference schemes that can be used to numerically integrate the time-dependent Schrodinger equation. These schemes are explicit and use an Euler-type expression for the discrete time derivative. However, the second-order space derivative is modeled by a novel form not