Fractional time-dependent Schrödinger equation on the Heisenberg group
✍ Scribed by Roman Urban; Jacek Zienkiewicz
- Publisher
- Springer-Verlag
- Year
- 2008
- Tongue
- French
- Weight
- 239 KB
- Volume
- 260
- Category
- Article
- ISSN
- 0025-5874
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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
Cheap and easy to implement fourth-order methods for the Schrodinger equation with time-dependent Hamiltonians are ïntroduced. The methods require evaluations of exponentials of simple unidimensional integrals, and can be considered an averaging technique, preserving many of the qualitative propert