Abstract
In the present paper we consider the semiclassical magnetic Schrödinger equation, which describes the dynamics of particles under the influence of a magnetic field. The solution of the time-dependent Schrödinger equation is approximated by a single Gaussian wave packet via the time-dependent Dirac-Frenkel variational principle. For the approximation we derive ordinary differential equations of motion for the parameters of the variational solution. Moreover, we prove L 2-error bounds and observable error bounds for the approximating Gaussian wave packet.
Original language | English |
---|---|
Article number | 295202 |
Journal | Journal of Physics A: Mathematical and Theoretical |
Volume | 57 |
Issue number | 29 |
DOIs | |
State | Published - 19 Jul 2024 |
Keywords
- magnetic Schrödinger equation
- observables
- semiclassical analysis
- variational approximation