Semiclassical Dynamics with Exponentially Small Error Estimates

Details Semiclassical Dynamics with Exponentially Small Error Estimates Semiclassical Dynamics with Exponentially Small Error Estimates

1998-12-23

arxiv.org/abs/math-ph/9812025v1

Physics

Mathematical Physics

Scientific paper

10.1007/s002200050732

We construct approximate solutions to the time--dependent Schr\"odinger equation $i \hbar (\partial \psi)/(\partial t) = - (\hbar^2)/2 \Delta \psi + V \psi$ for small values of $\hbar$. If $V$ satisfies appropriate analyticity and growth hypotheses and $|t|\le T$, these solutions agree with exact solutions up to errors whose norms are bounded by $C \exp{-\gamma/\hbar}$, for some $C$ and $\gamma>0$. Under more restrictive hypotheses, we prove that for sufficiently small $T', |t|\le T' |\log(\hbar)|$ implies the norms of the errors are bounded by $C' \exp{-\gamma'/\hbar^{\sigma}}$, for some $C', \gamma'>0$, and $\sigma>0$.

Affiliated with

Also associated with

No associations

Rating

Semiclassical Dynamics with Exponentially Small Error Estimates does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Semiclassical Dynamics with Exponentially Small Error Estimates, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Semiclassical Dynamics with Exponentially Small Error Estimates will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-11232