April 29, 2004
Nerd Heaven
I imagine every scientist and mathematician worth their sodium chloride already knows about this, but for interested layfolk, such as myself, this server is a revelation. I probably can't understand even the abstracts of 90% of these papers, but the wealth of scientific knowledge here is staggering.
You will find my paper under "Computational Physics" particularly interesting. I have found that exact solvability (typically, of harmonic oscillators) in quantum mechanics usually implies an elementary form of the spectrum while in all the "next-to-solvable" models, the energies E are only available in an implicit form (typically, as eigenvalues of an N-dimensional matrix). Therefore, I show that certain echoes of the unattainable harmonic-oscillator ideal may still survive in the latter (often called quasi-exact) cases exemplified here by the popular sextic anharmonic oscillator. In particular I show that whenever the spatial dimension D (or, equivalently, angular momentum L) happens to be "sufficiently" large, the surprisingly compact semi-explicit energies E remain available.
Big ups to my man mallarme for shoutin me out bitches!
guh?
He's talking about his paper on partial sums and optimal shifts in shifted large-L perturbation expansions for quasi-exact potentials, not the one on PT-symmetric regularizations in supersymmetric quantum mechanics. That probably explains your confusion, snw.
I go peepee standing up
My cat's breath smells like cat food.