Upper bounds to the overlap between approximate and exact wave functions

1970 ◽  
Vol 48 (14) ◽  
pp. 1681-1686 ◽  
Author(s):  
Maurice Cohen ◽  
Tova Feldmann
Keyword(s):  
Trial Function ◽  
Practical Method ◽  
Hamiltonian Operator ◽  
Upper Bounds ◽  
Wave Functions ◽  
Quantum Mechanical ◽  
Quantum Mechanical System ◽  
Lower And Upper Bounds ◽  
Present Procedure ◽  
Classical Procedure

Rigorous lower and upper bounds to the eigenvalues E of a quantum-mechanical system with Hamiltonian operator H are derived from the Gramian determinant of a set of suitably chosen functions. This procedure, which also yields a rigorous upper bound to the overlap between a given trial function and the corresponding (unknown) exact eigenfunction, is shown to be equivalent to a generalization of the classical procedure of Weinstein. In the absence of a rigorous lower bound to the overlap, the present procedure provides a practical method of assessing the influence of the ground state on a given trial function for an excited state.

Lower bounds to eigenvalues

1969 ◽  
Vol 47 (17) ◽  
pp. 1877-1879 ◽  
Author(s):  
Maurice Cohen ◽  
Tova Feldmann
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Upper Bound ◽  
Hamiltonian Operator ◽  
Upper And Lower Bounds ◽  
Quantum Mechanical ◽  
Classical Procedure ◽  
Ritz Procedure ◽  
Reasonable Choice ◽  
Lowest Eigenvalue

The classical procedure of Weinstein has been employed to obtain rigorous upper and lower bounds to the eigenvalues E of a quantum mechanical Hamiltonian operator H. The new bounds represent an improvement over Weinstein's bounds for any reasonable choice of variational trial function. In the case of the lowest eigenvalue E0, for which the Rayleigh–Ritz procedure gives the optimum upper bound, the new lower bound is an improvement over the lower bound formula of Stevenson and Crawford.

CONFORMAL PARASUPERSYMMETRY IN QUANTUM MECHANICS

1989 ◽  
Vol 04 (26) ◽  
pp. 2519-2529 ◽  
Author(s):  
STEPHANE DURAND ◽  
LUC VINET
Keyword(s):  
Quantum Mechanics ◽  
Energy Spectrum ◽  
Symmetry Algebra ◽  
Wave Functions ◽  
Quantum Mechanical ◽  
Quantum Mechanical System ◽  
One Dimensional ◽  
Complete Determination ◽  
Symmetry Generators

Conformal parasupersymmetry of order 2 is exemplified using a one-dimensional quantum mechanical system. Symmetry generators are seen to realize trilinear structure relations. The relevant representations of this novel symmetry algebra are constructed and shown to allow for a complete determination of the energy spectrum and wave functions of the system.

PHYSICAL PROJECTIONS IN BRST TREATMENTS OF REPARAMETRIZATION INVARIANT THEORIES

2001 ◽  
Vol 16 (17) ◽  
pp. 2909-2944
Author(s):  
ROBERT MARNELIUS ◽  
NICLAS SANDSTRÖM
Keyword(s):  
Invariant Theory ◽  
Brst Quantization ◽  
Wave Functions ◽  
Quantum Mechanical ◽  
Quantum Mechanical System ◽  
Path Integral Formulation ◽  
Abelian Gauge ◽  
Brst Charge ◽  
General Rules ◽  
Operator Version

Any regular quantum mechanical system may be cast into an Abelian gauge theory by simply reformulating it as a reparametrization invariant theory. We present a detailed study of the BRST quantization of such reparametrization invariant theories within a precise operator version of BRST which is related to the conventional BFV path integral formulation. Our treatments lead us to propose general rules for how physical wave functions and physical propagators are to be projected from the BRST singlets and propagators in the ghost extended BRST theory. These projections are performed by boundary conditions which are specified by the ingredients of BRST charge and precisely determined by the operator BRST. We demonstrate explicitly the validity of these rules for the considered class of models.

EXACT WAVE FUNCTIONS OF MULTI-SPECIES ANYON QUANTUM MECHANICS

1993 ◽  
Vol 08 (29) ◽  
pp. 5101-5113 ◽  
Author(s):  
K.H. CHO ◽  
CHAIHO RIM ◽  
D.S. SOH
Keyword(s):  
Magnetic Field ◽  
Quantum Mechanics ◽  
Angular Momentum ◽  
Wave Functions ◽  
Quantum Mechanical ◽  
Potential Well ◽  
Quantum Mechanical System ◽  
Ladder Operators ◽  
Free System ◽  
The Many

We investigate the many-anyon quantum-mechanical system of multi-species and obtain algebraically the energy and the angular momentum eigenstates in a harmonic potential well, in a constant magnetic field and of free system using ladder operators. The eigenvalues and their multiplicity of the eigenstates are given.

Trial Functions for the Two-Particle Density Functional Variational Method

1998 ◽  
Vol 53 (10-11) ◽  
pp. 833-840
Author(s):  
M. Gilles ◽  
H. Neumann ◽  
A. M. Popova
Keyword(s):  
Trial Function ◽  
Density Functional ◽  
Particle Density ◽  
Particle Interaction ◽  
Quantum Mechanical ◽  
Density Functions ◽  
Correlation Effects ◽  
Quantum Mechanical System ◽  
The Common ◽  
The One

Abstract The TV-particle quantum mechanical system in an external field is considered on the basis of two-particle density functions. The main point of the presented work is to reveal the advantages of the two-particle density formalism as compared to the common one-particle density formalism applied to a simple example. The two-particle density formalism permits us to take into account the exact two-particle interaction without additional models. The exchange and correlation effects can be considered by a proper choice of the trial function. By using the presented formalism we calculate the density of the electron gas on different metal surfaces. A simple trial function allowing for correlations gives us a more correct fit to the experimental data on the metal dipol barriers than corresponding calculations with the one-particle density formalism. It is also shown that a Pertubation of the external potential can be effectively taken into account by a Pertubation calculation for the trial function.

Extension of the Spatial PDI Model to Three Dimensions

1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien
Keyword(s):  
Population Density ◽  
Dimensional Space ◽  
Finite Lattice ◽  
Three Dimensional ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Lower And Upper Bounds ◽  
Density Index ◽  
Three Dimensional Space

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.

Energy of spherical fuzzy graphs

2020 ◽  
pp. 321-332
Author(s):  
S. Yahya Mohamed ◽  
A. Mohamed Ali
Keyword(s):  
Adjacency Matrix ◽  
Upper Bounds ◽  
Fuzzy Graph ◽  
Lower And Upper Bounds ◽  
Fuzzy Graphs

In this paper, the notion of energy extended to spherical fuzzy graph. The adjacency matrix of a spherical fuzzy graph is defined and we compute the energy of a spherical fuzzy graph as the sum of absolute values of eigenvalues of the adjacency matrix of the spherical fuzzy graph. Also, the lower and upper bounds for the energy of spherical fuzzy graphs are obtained.

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