Numerical study of energy-level crossing

Carl M. Bender; Henry J. Happ; Benjamin Svetitsky

doi:10.1103/PhysRevD.9.2324

Numerical study of energy-level crossing

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

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Pages (from-to)	2324-2329
Number of pages	6
Journal	Physical review D
Volume	9
Issue number	8
DOIs	https://doi.org/10.1103/PhysRevD.9.2324
State	Published - 1974
Externally published	Yes

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10.1103/PhysRevD.9.2324

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title = "Numerical study of energy-level crossing",

abstract = "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.",

author = "Bender, {Carl M.} and Happ, {Henry J.} and Benjamin Svetitsky",

note = "Funding Information: Work supported in part by the Fannie and John Hertz Foundation. Funding Information: Work supported in part by the MIT Student Information Processing Board.",

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doi = "10.1103/PhysRevD.9.2324",

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PY - 1974

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N2 - 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.

AB - 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.

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Numerical study of energy-level crossing

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