Physics:Variable-order fractional Schrödinger equation

From HandWiki

As a natural generalization of the fractional Schrödinger equation, the variable-order fractional Schrödinger equation has been exploited to study fractional quantum phenomena [1]

iψα(𝐫)(𝐫,t)tα(𝐫)=(2Δ)β(t)2ψ(𝐫,t)+V(𝐫,t)ψ(𝐫,t).

where Δ = 2/r2 is the Laplace operator and the operator (−ħ2Δ)β (t)/2 is the variable-order fractional quantum Riesz derivative.

References

  1. A. Bhrawy and M. Zaky, " An improved collocation method for multi-dimensional space-time variable-order fractional Schrödinger equations”, Applied Numerical Mathematics, Volume 111, January 2017, Pages 197–218 [1]