### Abstract

By using the continual direct-sum decomposition obtained previously for the t operators, it is shown that the change of the density of states in the presence of a general (non-muffin-tin) periodic potential can be given in a determinant form involving only the on-shell t matrix. The result obtained is close to the usual Friedel sum rule of scattering theory which, however, relies strongly on the existence of asymptotic free motion and hence, on the existence of the phase-shift motion. Thus, since the periodic potential does not allow for the existence of asymptotic free motion, the present result illustrates a rather general trace property of the resolvent, which appears to be independent of the very different boundary conditions in the two cases.

Original language | English |
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Pages (from-to) | 1401-1405 |

Number of pages | 5 |

Journal | Physical Review B |

Volume | 36 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1987 |

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### ASJC Scopus subject areas

- Condensed Matter Physics

### Cite this

*Physical Review B*,

*36*(3), 1401-1405. https://doi.org/10.1103/PhysRevB.36.1401

**Friedel-type sum rule for a general periodic potential.** / Badralexe, E.; Freeman, Arthur J.

Research output: Contribution to journal › Article

*Physical Review B*, vol. 36, no. 3, pp. 1401-1405. https://doi.org/10.1103/PhysRevB.36.1401

}

TY - JOUR

T1 - Friedel-type sum rule for a general periodic potential

AU - Badralexe, E.

AU - Freeman, Arthur J

PY - 1987

Y1 - 1987

N2 - By using the continual direct-sum decomposition obtained previously for the t operators, it is shown that the change of the density of states in the presence of a general (non-muffin-tin) periodic potential can be given in a determinant form involving only the on-shell t matrix. The result obtained is close to the usual Friedel sum rule of scattering theory which, however, relies strongly on the existence of asymptotic free motion and hence, on the existence of the phase-shift motion. Thus, since the periodic potential does not allow for the existence of asymptotic free motion, the present result illustrates a rather general trace property of the resolvent, which appears to be independent of the very different boundary conditions in the two cases.

AB - By using the continual direct-sum decomposition obtained previously for the t operators, it is shown that the change of the density of states in the presence of a general (non-muffin-tin) periodic potential can be given in a determinant form involving only the on-shell t matrix. The result obtained is close to the usual Friedel sum rule of scattering theory which, however, relies strongly on the existence of asymptotic free motion and hence, on the existence of the phase-shift motion. Thus, since the periodic potential does not allow for the existence of asymptotic free motion, the present result illustrates a rather general trace property of the resolvent, which appears to be independent of the very different boundary conditions in the two cases.

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U2 - 10.1103/PhysRevB.36.1401

DO - 10.1103/PhysRevB.36.1401

M3 - Article

VL - 36

SP - 1401

EP - 1405

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 1098-0121

IS - 3

ER -