Phase Space Approach to Solving the Time-independent Schrödinger Equation

Details Phase Space Approach to Solving the Time-independent Schrödinger Equation Phase Space Approach to Solving the Time-independent Schrödinger Equation

2012-01-11

arxiv.org/abs/1201.2299v1

Physics

Quantum Physics

5 figures. Includes supplementary material. arXiv admin note: substantial text overlap with arXiv:1010.2588

Scientific paper

We propose a method for solving the time independent Schr\"odinger equation based on the von Neumann (vN) lattice of phase space Gaussians. By incorporating periodic boundary conditions into the vN lattice [F. Dimler et al., New J. Phys. 11, 105052 (2009)] we solve a longstanding problem of convergence of the vN method. This opens the door to tailoring quantum calculations to the underlying classical phase space structure while retaining the accuracy of the Fourier grid basis. The method has the potential to provide enormous numerical savings as the dimensionality increases. In the classical limit the method reaches the remarkable efficiency of 1 basis function per 1 eigenstate. We illustrate the method for a challenging two-dimensional potential where the FGH method breaks down.

Affiliated with

Also associated with

No associations

Rating

Phase Space Approach to Solving the Time-independent Schrödinger Equation 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 Phase Space Approach to Solving the Time-independent Schrödinger Equation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Phase Space Approach to Solving the Time-independent Schrödinger Equation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-604248