Maximizing the hyperpolarizability poorly determines the potential

Details Maximizing the hyperpolarizability poorly determines the potential Maximizing the hyperpolarizability poorly determines the potential

2010-10-23

arxiv.org/abs/1010.4919v2

Physics

Chemical Physics

18 pages, 3 figures

Scientific paper

We have optimized the zero frequency first hyperpolarizability \beta of a one-dimensional piecewise linear potential well containing a single electron by adjusting the shape of that potential. With increasing numbers of parameters in the potential, the maximized hyperpolarizability converges quickly to 0.708951 of the proven upper bound. The Hessian of \beta at the maximum has in each case only two large eigenvalues; the other eigenvalues diminish seemingly exponentially quickly, demonstrating a very wide range of nearby nearly optimal potentials, and that there are only two important parameters for optimizing \beta. The shape of the optimized wavefunctions converges with more parameters while the associated potentials remain substantially different, suggesting that the ground state wavefunction provides a superior physical description to the potential for the conditions that optimize the hyperpolarizability. Prospects for characterizing the two important parameters for near-optimum potentials are discussed.

Affiliated with

Also associated with

No associations

Rating

Maximizing the hyperpolarizability poorly determines the potential 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 Maximizing the hyperpolarizability poorly determines the potential, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Maximizing the hyperpolarizability poorly determines the potential will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-277068