### Abstract

The finite size scaling ansatz is combined with the variational method to extract information about critical behavior of quantum Hamiltonians. This approach is based on taking the number of elements in a complete basis set as the size of the system. As in statistical mechanics, the finite size scaling can then be used directly in the Schrödinger equation. This approach is general and gives very accurate results for the critical parameters, for which the bound-state energy becomes absorbed or degenerate with a continuum. To illustrate the applications in quantum calculations, we present detailed calculations for both short- and long-range potentials.

Original language | English |
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Pages (from-to) | 9518-9522 |

Number of pages | 5 |

Journal | Journal of Physical Chemistry A |

Volume | 102 |

Issue number | 47 |

Publication status | Published - 19 Nov 1998 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Physical and Theoretical Chemistry

### Cite this

*Journal of Physical Chemistry A*,

*102*(47), 9518-9522.

**Finite size scaling in quantum mechanics.** / Serra, Pablo; Neirotti, Juan Pablo; Kais, Sabre.

Research output: Contribution to journal › Article

*Journal of Physical Chemistry A*, vol. 102, no. 47, pp. 9518-9522.

}

TY - JOUR

T1 - Finite size scaling in quantum mechanics

AU - Serra, Pablo

AU - Neirotti, Juan Pablo

AU - Kais, Sabre

PY - 1998/11/19

Y1 - 1998/11/19

N2 - The finite size scaling ansatz is combined with the variational method to extract information about critical behavior of quantum Hamiltonians. This approach is based on taking the number of elements in a complete basis set as the size of the system. As in statistical mechanics, the finite size scaling can then be used directly in the Schrödinger equation. This approach is general and gives very accurate results for the critical parameters, for which the bound-state energy becomes absorbed or degenerate with a continuum. To illustrate the applications in quantum calculations, we present detailed calculations for both short- and long-range potentials.

AB - The finite size scaling ansatz is combined with the variational method to extract information about critical behavior of quantum Hamiltonians. This approach is based on taking the number of elements in a complete basis set as the size of the system. As in statistical mechanics, the finite size scaling can then be used directly in the Schrödinger equation. This approach is general and gives very accurate results for the critical parameters, for which the bound-state energy becomes absorbed or degenerate with a continuum. To illustrate the applications in quantum calculations, we present detailed calculations for both short- and long-range potentials.

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UR - http://www.scopus.com/inward/citedby.url?scp=0006789264&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0006789264

VL - 102

SP - 9518

EP - 9522

JO - Journal of Physical Chemistry A

JF - Journal of Physical Chemistry A

SN - 1089-5639

IS - 47

ER -