scholarly journals Hadron spectroscopy using the light-front holographic Schrödinger equation and the ’t Hooft equation

2021 ◽  
Vol 104 (7) ◽  
Author(s):  
Mohammad Ahmady ◽  
Sugee Lee MacKay ◽  
Satvir Kaur ◽  
Chandan Mondal ◽  
Ruben Sandapen
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Light Front ◽  
Hadron Spectroscopy

scholarly journals Two Schrödinger-like Equations for hadrons

2022 ◽  
Vol 258 ◽  
pp. 10009
Author(s):  
Ruben Sandapen
Keyword(s):  
Schrödinger Equation ◽  
Atomic Physics ◽  
Schrodinger Equation ◽  
Light Front ◽  
Hadronic Physics ◽  
Hadron Spectroscopy ◽  
First Approximation

In this talk, based on [1, 2], I argue that the holographic Schrödinger Equation of (3 +1)-dim, conformal light-front QCD and the ’t Hooft Equation of (1+1)-dim, large Nc QCD, can be complementary to each other in providing a first approximation to hadron spectroscopy. Together, the two equations play a role in hadronic physics analogous that of the ordinary Schrödinger Equation in atomic physics.

scholarly journals LIGHT-FRONT HOLOGRAPHY AND THE LIGHT-FRONT SCHRÖDINGER EQUATION

2012 ◽  
Vol 20 ◽  
pp. 53-65 ◽  
Author(s):  
STANLEY J. BRODSKY ◽  
GUY DE TÉRAMOND
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Bound States ◽  
Light Quark ◽  
Form Factors ◽  
Light Front ◽  
Hadron Structure ◽  
Hadron Spectrum ◽  
Excitation Spectra ◽  
Fifth Dimension

One of the most important nonperturbative methods for solving QCD is quantization at fixed light-front time τ = t + z/c – Dirac's "Front Form". The eigenvalues of the light-front QCD Hamiltonian predict the hadron spectrum and the eigensolutions provide the light-front wavefunctions which describe hadron structure. More generally, we show that the valence Fock-state wavefunctions of the light-front QCD Hamiltonian satisfy a single-variable relativistic equation of motion, analogous to the nonrelativistic radial Schrödinger equation, with an effective confining potential U which systematically incorporates the effects of higher quark and gluon Fock states. We outline a method for computing the required potential from first principles in QCD. The holographic mapping of gravity in AdS space to QCD, quantized at fixed light-front time, yields the same light front Schrödinger equation; in fact, the soft-wall AdS/QCD approach provides a model for the light-front potential which is color-confining and reproduces well the light-hadron spectrum. One also derives via light-front holography a precise relation between the bound-state amplitudes in the fifth dimension of AdS space and the boost-invariant light-front wavefunctions describing the internal structure of hadrons in physical space-time. The elastic and transition form factors of the pion and the nucleons are found to be well described in this framework. The light-front AdS/QCD holographic approach thus gives a frame-independent first approximation of the color-confining dynamics, spectroscopy, and excitation spectra of relativistic light-quark bound states in QCD.

scholarly journals Light-front holographic QCD and color confinement

2014 ◽  
Vol 29 (21) ◽  
pp. 1444013 ◽  
Author(s):  
Stanley J. Brodsky ◽  
Guy F. de Teramond ◽  
Hans Günter Dosch
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Dimensional Space ◽  
Form Factors ◽  
Mass Scale ◽  
Light Front ◽  
Classical Level ◽  
Conformally Invariant ◽  
Color Confinement ◽  
Soft Wall Model

One of the most fundamental problems in Quantum Chromodynamics is to understand the origin of the mass scale which controls the range of color confinement and the hadronic spectrum. For example, if one sets the Higgs couplings of quarks to zero, then no mass parameters appear in the QCD Lagrangian, and the theory is conformal at the classical level. Nevertheless, hadrons have a finite mass. We show that a mass gap and a fundamental color confinement scale arise when one extends the formalism of de Alfaro, Fubini and Furlan (dAFF) to frame-independent light-front Hamiltonian theory. Remarkably, the resulting light-front potential has a unique form of a harmonic oscillator in the light-front invariant impact variable if one requires that the action remains conformally invariant. The result is a single-variable relativistic equation of motion for [Formula: see text] bound states, a "Light-Front Schrödinger Equation," analogous to the nonrelativistic radial Schrödinger equation, which incorporates color confinement and other essential spectroscopic and dynamical features of hadron physics, including a massless pion for zero quark mass and linear Regge trajectories with the same slope in the radial quantum number and orbital angular momentum. The same light-front equations with the correct hadron spin dependence arise from the holographic mapping of "soft-wall model" modification of AdS5 space with a specific dilaton profile. The corresponding light-front Dirac equation provides a dynamical and spectroscopic model of nucleons. A fundamental mass parameter κ appears, determining the hadron masses and the length scale which underlies hadron structure. Quark masses can be introduced to account for the spectrum of strange hadrons. This Light-Front Holographic approach predicts not only hadron spectroscopy successfully, but also hadron dynamics — hadronic form factors, the QCD running coupling at small virtuality, the light-front wavefunctions of hadrons, ρ electroproduction, distribution amplitudes, valence structure functions, etc. Thus the combination of light-front dynamics, its holographic mapping to gravity in a higher-dimensional space and the dAFF procedure provides new insight into the physics underlying color confinement, chiral invariance, and the QCD mass scale, among the most profound questions in physics.

Solusi Persamaan Schrödinger Berbasis Panjang Minimal untuk Potensial Coulomb Termodifikasi

2018 ◽  
Vol 2 (2) ◽  
pp. 43-47
Author(s):  
A. Suparmi, C. Cari, Ina Nurhidayati
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Coulomb Potential ◽  
Schrodinger Equation ◽  
Minimal Length ◽  
Energy Spectra ◽  
Atomic Particle ◽  
Approximate Analytical Solutions ◽  
Radial Schrödinger Equation

Abstrak – Persamaan Schrödinger adalah salah satu topik penelitian yang yang paling sering diteliti dalam mekanika kuantum. Pada jurnal ini persamaan Schrödinger berbasis panjang minimal diaplikasikan untuk potensial Coulomb Termodifikasi. Fungsi gelombang dan spektrum energi yang dihasilkan menunjukkan kharakteristik atau tingkah laku dari partikel sub atom. Dengan menggunakan metode pendekatan hipergeometri, diperoleh solusi analitis untuk bagian radial persamaan Schrödinger berbasis panjang minimal diaplikasikan untuk potensial Coulomb Termodifikasi. Hasil yang diperoleh menunjukkan terjadi peningkatan energi yang sebanding dengan meningkatnya parameter panjang minimal dan parameter potensial Coulomb Termodifikasi. Kata kunci: persamaan Schrödinger, panjang minimal, fungsi gelombang, energi, potensial Coulomb Termodifikasi Abstract – The Schrödinger equation is the most popular topic research at quantum mechanics. The  Schrödinger equation based on the concept of minimal length formalism has been obtained for modified Coulomb potential. The wave function and energy spectra were used to describe the characteristic of sub-atomic particle. By using hypergeometry method, we obtained the approximate analytical solutions of the radial Schrödinger equation based on the concept of minimal length formalism for the modified Coulomb potential. The wave function and energy spectra was solved. The result showed that the value of energy increased by the increasing both of minimal length parameter and the potential parameter. Key words: Schrödinger equation, minimal length formalism (MLF), wave function, energy spectra, Modified Coulomb potential

Introduction

2018 ◽  
Author(s):  
Niels Engholm Henriksen ◽  
Flemming Yssing Hansen
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Degrees Of Freedom ◽  
State Level ◽  
Boltzmann Distribution ◽  
Theoretical Description ◽  
Time Dependent ◽  
Nuclear Dynamics ◽  
Molecular Reaction ◽  
Oppenheimer Approximation

This introductory chapter considers first the relation between molecular reaction dynamics and the major branches of physical chemistry. The concept of elementary chemical reactions at the quantized state-to-state level is discussed. The theoretical description of these reactions based on the time-dependent Schrödinger equation and the Born–Oppenheimer approximation is introduced and the resulting time-dependent Schrödinger equation describing the nuclear dynamics is discussed. The chapter concludes with a brief discussion of matter at thermal equilibrium, focusing at the Boltzmann distribution. Thus, the Boltzmann distribution for vibrational, rotational, and translational degrees of freedom is discussed and illustrated.

Quantum Boxes, Stringed Instruments

2017 ◽  
Author(s):  
Frank S. Levin
Keyword(s):  
Energy Level ◽  
Schrödinger Equation ◽  
Quantum System ◽  
Schrodinger Equation ◽  
Probability Distributions ◽  
Wave Functions ◽  
Energy Level Diagram ◽  
One Dimensional ◽  
Stringed Instruments ◽  
Symmetry Properties

Chapter 7 illustrates the results obtained by applying the Schrödinger equation to a simple pedagogical quantum system, the particle in a one-dimensional box. The wave functions are seen to be sine waves; their wavelengths are evaluated and used to calculate the quantized energies via the de Broglie relation. An energy-level diagram of some of the energies is constructed; on it are illustrations of the corresponding wave functions and probability distributions. The wave functions are seen to be either symmetric or antisymmetric about the midpoint of the line representing the box, thereby providing a lead-in to the later exploration of certain symmetry properties of multi-electron atoms. It is next pointed out that the Schrödinger equation for this system is identical to Newton’s equation describing the vibrations of a stretched musical string. The different meaning of the two solutions is discussed, as is the concept and structure of linear superpositions of them.

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