### Abstract

In Part A, a further analysis is made of the collective coordinate Lagrangian first introduced in a previous paper. This Lagrangian, which replaces the physical Lagrangian, describes a set of fictitious harmonic oscillators whose masses and frequencies are established. We accomplish this by adding a term to the physical Lagrangian which, however, does not affect the equations of motion. The analysis is carried out by two distinct methods: comparison of Lagrangians and comparison of equations of motion. Both methods yield identical results. In Part B, the difficult problem of representing the Dirac δ function by a finite number of terms is handled by the introduction of the d-function. A specific representation of this function is given, along with plausibility arguments that it satisfies the requirements of Part A. A brief analysis and summary of the manifold properties of the d-function is presented.

Original language | English (US) |
---|---|

Pages (from-to) | 1192-1197 |

Number of pages | 6 |

Journal | Physical Review |

Volume | 101 |

Issue number | 3 |

DOIs | |

State | Published - 1956 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Physical Review*,

*101*(3), 1192-1197. https://doi.org/10.1103/PhysRev.101.1192

**Dynamical considerations on a new approach to the many-body problem.** / Percus, Jerome; Yevick, George J.

Research output: Contribution to journal › Article

*Physical Review*, vol. 101, no. 3, pp. 1192-1197. https://doi.org/10.1103/PhysRev.101.1192

}

TY - JOUR

T1 - Dynamical considerations on a new approach to the many-body problem

AU - Percus, Jerome

AU - Yevick, George J.

PY - 1956

Y1 - 1956

N2 - In Part A, a further analysis is made of the collective coordinate Lagrangian first introduced in a previous paper. This Lagrangian, which replaces the physical Lagrangian, describes a set of fictitious harmonic oscillators whose masses and frequencies are established. We accomplish this by adding a term to the physical Lagrangian which, however, does not affect the equations of motion. The analysis is carried out by two distinct methods: comparison of Lagrangians and comparison of equations of motion. Both methods yield identical results. In Part B, the difficult problem of representing the Dirac δ function by a finite number of terms is handled by the introduction of the d-function. A specific representation of this function is given, along with plausibility arguments that it satisfies the requirements of Part A. A brief analysis and summary of the manifold properties of the d-function is presented.

AB - In Part A, a further analysis is made of the collective coordinate Lagrangian first introduced in a previous paper. This Lagrangian, which replaces the physical Lagrangian, describes a set of fictitious harmonic oscillators whose masses and frequencies are established. We accomplish this by adding a term to the physical Lagrangian which, however, does not affect the equations of motion. The analysis is carried out by two distinct methods: comparison of Lagrangians and comparison of equations of motion. Both methods yield identical results. In Part B, the difficult problem of representing the Dirac δ function by a finite number of terms is handled by the introduction of the d-function. A specific representation of this function is given, along with plausibility arguments that it satisfies the requirements of Part A. A brief analysis and summary of the manifold properties of the d-function is presented.

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U2 - 10.1103/PhysRev.101.1192

DO - 10.1103/PhysRev.101.1192

M3 - Article

AN - SCOPUS:36149016045

VL - 101

SP - 1192

EP - 1197

JO - Physical Review

JF - Physical Review

SN - 0031-899X

IS - 3

ER -