Finite Size Scaling in Quantum Mechanics

PABLO SERRA; JUAN PABLO NEIROTTI; SABRE KAIS

JOURNAL OF PHYSICAL CHEMISTRY A

AMER CHEMICAL SOC

Lugar: Washington; Año: 1998 vol. 102 p. 9518 - 9522

1089-5639

The finite size scaling ansatz is combined with the variational method to extract information about criticalbehavior of quantum Hamiltonians. This approach is based on taking the number of elements in a completebasis set as the size of the system. As in statistical mechanics, the finite size scaling can then be used directlyin the Schrodinger  ̈ 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 theapplications in quantum calculations, we present detailed calculations for both short- and long-range potentials.