Numerical study of energy-level crossing

Carl M. Bender*, Henry J. Happ, Benjamin Svetitsky

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We use a rapidly convergent numerical method recently proposed by Graffi and Grecchi to study the analytic properties of the eigenvalues E(ε) of the differential equation [-(d2dx2)+ε|x|+14x2-E(ε)]ψ(x)=0, lim|x|→ψ(x)=0. We analytically continue E(ε) into the complex ε plane on a computer, demonstrate graphically the phenomenon of level crossing, and show that the crossing points are square-root branch points.

Original languageEnglish
Pages (from-to)2324-2329
Number of pages6
JournalPhysical review D
Issue number8
StatePublished - 1974
Externally publishedYes


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