Amaury Mouchet 2005 J. Phys. A: Math. Gen. 38 1039 doi:10.1088/0305-4470/38/5/006
A differential method for bounding the ground state energy
Amaury Mouchet
Show affiliationsFor a wide class of Hamiltonians, a novel method for obtaining lower and upper bounds for the lowest energy is presented. Unlike perturbative or variational techniques, this method does not involve the computation of any integral (a normalization factor or a matrix element). It just requires the determination of the absolute minimum and maximum in the whole configuration space of the local energy associated with a normalizable trial function (the calculation of the norm is not needed). After a general introduction, the method is applied to three non-integrable systems: the asymmetric annular billiard, the many-body spinless Coulombian problem, the hydrogen atom in a constant and uniform magnetic field. Being more sensitive than the variational methods to any local perturbation of the trial function, this method can be used to systematically improve the energy bounds with a local skilled analysis; an algorithm relying on this method can therefore be constructed and an explicit example for a one-dimensional problem is given.
- PACS
- MSC
-
81Qxx General mathematical topics and methods in quantum theory
- Subjects
- Dates
-
Issue 5 (4 February 2005)
Received 20 October 2004, in final form 25 November 2004
Published 19 January 2005
-
A differential method for bounding the ground state energy
Amaury Mouchet 2005 J. Phys. A: Math. Gen. 38 1039
-
Pseudo-Spin-Valve Trilayer Using Amorphous CoNbZr Layer: Giant Magnetoresistance, Domain Structures and Potentials for Spin-Electronic Devices
Wen Qi-Ye et al 2004 Chinese Phys. Lett. 21 941
-
Major applications of electrochemical techniques at national metrology institutes
Michal Máriássy et al 2009 Metrologia 46 199
-
Some systematics of the coupling constant dependence of N = 4 Yang-Mills
Anirban Basu et al JHEP09(2004)045
-
Hidden symmetries and black holes
Valeri P Frolov 2009 J. Phys.: Conf. Ser. 189 012015
-
Spectroscopy of z ~ 6 i-Dropout Galaxies: Frequency of Lyα Emission and the Sizes of Lyα-emitting Galaxies
C. C. Dow-Hygelund et al. 2007 ApJ 660 47
-
The convolution method for calculations of local densities of states
A Losev 2003 J. Phys.: Condens. Matter 15 1007
-
Coherent acoustic oscillations of nanoscale Au triangles and pyramids: influence of size and substrate
R Taubert et al 2007 New J. Phys. 9 376
-
Uncertainties on distance and chromatic dispersion measurement using optical low-coherence reflectometry
A-F Obaton et al 2008 Metrologia 45 83
-
Uncertainty budget for the NIST electron counting capacitance standard, ECCS-1
Mark W Keller et al 2007 Metrologia 44 505
Related review articles
What's this?- Integrable structure of box–ball systems: crystal, Bethe ansatz, ultradiscretization and tropical geometry
- Spectral problems in open quantum chaos
- Lectures on localization and matrix models in supersymmetric Chern–Simons-matter theories
super-Yang–Mills*