Exact sum rules for inhomogeneous systems containing a zero mode

Amore, Paolo

doi:10.1016/J.AOP.2014.06.019

Title: Exact sum rules for inhomogeneous systems containing a zero mode

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Abstract

We show that the formulas for the sum rules for the eigenvalues of inhomogeneous systems that we have obtained in two recent papers are incomplete when the system contains a zero mode. We prove that there are finite contributions of the zero mode to the sum rules and we explicitly calculate the expressions for the sum rules of order one and two. The previous results for systems that do not contain a zero mode are unaffected. - Highlights: • We discuss the sum rules of the eigenvalues of inhomogeneous systems containing a zero mode. • We derive the explicit expressions for sum rules of order one and two. • We perform accurate numerical tests of these results for three examples.

Authors:: Amore, Paolo

Publication Date:: Wed Oct 15 00:00:00 EDT 2014

OSTI Identifier:: 22403412

Resource Type:: Journal Article

Journal Name:: Annals of Physics (New York)

Additional Journal Information:: Journal Volume: 349; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0003-4916

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; EIGENVALUES; NUMERICAL ANALYSIS; SUM RULES

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                    Amore, Paolo. Exact sum rules for inhomogeneous systems containing a zero mode.  United States: N. p., 2014. 
        Web.  doi:10.1016/J.AOP.2014.06.019.

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                    Amore, Paolo. Exact sum rules for inhomogeneous systems containing a zero mode.  United States.  https://doi.org/10.1016/J.AOP.2014.06.019

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                    Amore, Paolo. 2014.  
        "Exact sum rules for inhomogeneous systems containing a zero mode".  United States.  https://doi.org/10.1016/J.AOP.2014.06.019.

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@article{osti_22403412,

  title        = {Exact sum rules for inhomogeneous systems containing a zero mode},

  author       = {Amore, Paolo},

  abstractNote = {We show that the formulas for the sum rules for the eigenvalues of inhomogeneous systems that we have obtained in two recent papers are incomplete when the system contains a zero mode. We prove that there are finite contributions of the zero mode to the sum rules and we explicitly calculate the expressions for the sum rules of order one and two. The previous results for systems that do not contain a zero mode are unaffected. - Highlights: • We discuss the sum rules of the eigenvalues of inhomogeneous systems containing a zero mode. • We derive the explicit expressions for sum rules of order one and two. • We perform accurate numerical tests of these results for three examples.},

  doi          = {10.1016/J.AOP.2014.06.019},

  url          = {https://www.osti.gov/biblio/22403412},
  journal      = {Annals of Physics (New York)},

  issn         = {0003-4916},

  number       = ,

  volume       = 349,

  place        = {United States},

  year         = {Wed Oct 15 00:00:00 EDT 2014},

  month        = {Wed Oct 15 00:00:00 EDT 2014}

}

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