scholarly journals SHORT DISTANCE REPULSION AMONG BARYONS

2013 ◽  
Vol 22 (05) ◽  
pp. 1330012 ◽  
Author(s):  
SINYA AOKI ◽  
JANOS BALOG ◽  
TAKUMI DOI ◽  
TAKASHI INOUE ◽  
PETER WEISZ
Keyword(s):  
Wave Function ◽  
Perturbation Theory ◽  
Renormalization Group ◽  
Lattice Qcd ◽  
Operator Product Expansion ◽  
Short Distance ◽  
Numerical Results ◽  
Wave Functions ◽  
Operator Product ◽  
Distance Behavior

We review recent investigations on the short distance behaviors of potentials among baryons, which are formulated through the Nambu–Bethe–Salpeter (NBS) wave function. After explaining the method to define the potentials, we analyze the short distance behavior of the NBS wave functions and the corresponding potentials by combining the operator product expansion (OPE) and a renormalization group (RG) analysis in the perturbation theory (PT) of QCD. These analytic results are compared with numerical results obtained in lattice QCD simulations.

NEW SCALING VARIABLE FROM LIGHT-CONE PERTURBATION THEORY

1991 ◽  
Vol 06 (03) ◽  
pp. 345-363 ◽  
Author(s):  
BO-QIANG MA ◽  
JI SUN
Keyword(s):  
Perturbation Theory ◽  
Power Law ◽  
Light Cone ◽  
Operator Product Expansion ◽  
Free Field ◽  
Field Operator ◽  
Order Effect ◽  
Operator Product ◽  
Bjorken Scaling ◽  
Twist Effect

We argue from both the quark language and the free field light-cone expansion in light-cone perturbation theory that the constraint of overall “energy” conservation in deep inelastic lepton-nucleon scattering yields a similar new scaling variable xp, which reduces to the Weizmann variable, the Bloom-Gilman variable and the Bjorken variable at some approximations. The xp rescaling is expected to be a good scaling variable, and hence gives strong power-law type corrections to the deviations of Bjorken scaling. An understanding of this xp rescaling from both the free field operator product expansion (OPE) and the ordinary OPE is also given, indicating it is likely a higher order effect in the coefficient functions, i.e. it does not belong to the higher twist effect. Therefore this xp rescaling is likely a new effect contributing to the power-law type corrections.

The Polarizability of Molecular Hydrogen H2

1936 ◽  
Vol 32 (2) ◽  
pp. 260-264 ◽  
Author(s):  
C. E. Easthope
Keyword(s):  
Wave Function ◽  
Perturbation Theory ◽  
Molecular Hydrogen ◽  
Applied Field ◽  
Minimum Energy ◽  
Wave Functions ◽  
The Other ◽  
System A ◽  
The One ◽  
Two Parameter

1. The problem of calculating the polarizability of molecular hydrogen has recently been considered by a number of investigators. Steensholt and Hirschfelder use the variational method developed by Hylleras and Hassé. For ψ0, the wave function of the unperturbed molecule when no external field is present, they take either the Rosent or the Wang wave function, while the wave functions of the perturbed molecule were considered in both the one-parameter form, ψ0 [1+A(q1 + q2)] and the two-parameter form, ψ0 [1+A(q1 + q2) + B(r1q1 + r2q2)], where A and B are parameters to be varied so as to give the system a minimum energy, q1 and q2 are the coordinates of the electrons 1 and 2 in the direction of the applied field as measured from the centre of the molecule, and r1 and r2 are their respective distances from the same point. Mrowka, on the other hand, employs a method based on the usual perturbation theory. Their numerical results are given in the following table.

scholarly journals SCHRÖDINGER EQUATION FOR HEAVY MESONS EXPANDED IN 1/mQ

1996 ◽  
Vol 11 (03) ◽  
pp. 257-266 ◽  
Author(s):  
TAKAYUKI MATSUKI
Keyword(s):  
Wave Function ◽  
Perturbation Theory ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Bound States ◽  
Higher Order ◽  
Wave Functions ◽  
Heavy Mesons ◽  
Higher Order Corrections

Operating just once the naive Foldy-Wouthuysen-Tani transformation on the Schrödinger equation for [Formula: see text] bound states described by a Hamiltonian, we systematically develop a perturbation theory in 1/mQ which enables one to solve the Schrödinger equation to obtain masses and wave functions of the bound states in any order of 1/mQ. There also appear negative components of the wave function in our formulation which contribute also to higher order corrections to masses.

Hypervirial theorems and perturbation theory in quantum mechanics

1965 ◽  
Vol 283 (1393) ◽  
pp. 229-237 ◽  
Keyword(s):  
Wave Function ◽  
Perturbation Theory ◽  
Wave Functions ◽  
First Order ◽  
Optimum Energy ◽  
Arbitrary Operator ◽  
Approximate Wave Function ◽  
Hypervirial Theorem ◽  
Variational Wave Functions ◽  
Approximate Wave

Previous ideas about the way in which hypervirial theorems might be used to improve approximate wave functions are discussed. To provide a firmer foundation for these ideas, a link is established between hypervirial theorems and perturbation theory. It is proved that if the first-order perturbation correction to the expectation value of an arbitrary operator vanishes, then the approximate wave function used satisfies a certain hypervirial theorem. Conversely, if an arbitrary hypervirial theorem is satisfied by the wave function, then it is proved that the expectation values of certain operators have vanishing first-order corrections. Some consequences of the theory as applied to variational wave functions with optimum energy are developed. The results are illustrated by the use of a simple approximate wave function for the ground state of the helium atom.

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