Wave equation the purpose of these lectures is to give a basic introduction to the study of linear wave equation. This describes the potential for a force mediated by massless particles, the photons. The wave equation governs a wide range of phenomena, including gravitational waves, light waves, sound waves, and even the oscillations of strings in string theory. In this work, we introduce a novel potential in the form of a yukawa potential very similar to the combinations of the iqy potential 25 and yukawa potential 46 i. Yukawas potential, schrodinger equation, whittakers. Physics 216 spring 2012 quantum mechanics of a charged. On the longwaves dispersion in yukawa systems sergey a. Coulombic and for a harmonic oscillator represent two typical examples in quantum. This paper is a didactic exploration of the rationale for such wave equation.
The mathematics of pdes and the wave equation michael p. A solution to the wave equation in two dimensions propagating over a fixed region 1. We study the ground state energy and the critical screening parameter of the yukawa potential in nonrelativistic quantum mechanics. Relation of gammaray and yukawa wave function, wave equation. Using the separation method with the wave function. The wave equation is a secondorder linear hyperbolic pde that describesthe propagation of a variety of waves, such as sound or water waves. Yukawa potential and coulomb potential which we con. There are one way wave equations, and the general solution to the two way equation could be done by forming linear combinations of such solutions. The manningrosen plus a class of yukawa potential takes the form. The weak interaction is transmitted by such kind of vector bosons. Solutions to the schrodinger equation with inversely. With the introduction of the iqyiqh potential into the schrodinger equation, the resultant equation is further transformed in such a way that certain polynomials with four different possible forms are obtained. Pdf eigensolutions of the schrodinger equation with a class of. Out of equilibrium twodimensional yukawa theory in a strong scalar wave background e.
Assuming that the spacetime consists of elementary domains proposed by yukawa, we attempt to extend the stochastic quantization procedures introduced by nelson in the nonrelativistic case to the relativistic one. These notes present the schrodinger equation for a charged particle in an external electromagnetic. We calculate wave function of the dirac equation for a new form of yukawa potential, including a coulomblike tensor potential. Scattering theory scattering theory is important as it underpins one of the most ubiquitous tools in physics. Pdf scattering and bound state solutions of the yukawa potential. Jean louis van belle, drs, maec, baec, bphil 23 june 2019 abstract one can think of a wave equation for the nucleus based on the yukawa potential. Energy levels of spin12 particles with yukawa interaction. The wave equation is a linear secondorder partial differential equation which describes the propagation of oscillations at a fixed speed in some quantity y y y. Out of equilibrium twodimensional yukawa theory in a. Pdf in the presence of spin symmetry case, we obtain bound and scattering states. Analytical solution to the yukawas potential using. Rutherfords discovery of the nucleus, the discovery of subatomic particles such as quarks, etc. The potential describing tensor interaction has a yukawalike form.
Derivation of relativistic wave equations in the theory of. We then use this result to obtain the schrodinger equation using the principle of minimal substitution. The equation then yields a form whose polynomial solutions are given by the wellknown rodrigues relation. In particle, atomic and condensed matter physics, a yukawa potential also called a screened coulomb potential is a potential of the form.
The equation of motion that follows from this action is. Depending on the medium and type of wave, the velocity v v v can mean many different things, e. July 20, 2010 we derive a new integral equation that allows the calculation of the scattering or annihilation amplitude of two particles subjected to two potentials when the. An integral equation for distorted wave amplitudes luca visinelli. An integral equation for distorted wave amplitudes pdf.
Scattering and bound state solutions of the yukawa potential. We show how the second order wave equation can be decomposed into two. In particular, we examine questions about existence and. University of calgary seismic imaging summer school august 711, 2006, calgary abstract abstract. Approximate analytical solution of the yukawa potential with. In this work, we have studied bound state and scattering state of the dirac equation with the yukawa potential. The relation, introduction wave functions for the deuteron, assumed to be bound by a yukawa potential, have been calculated essentially in two ways. Bound state spectrum and wave functions of yukawa potential are obtained. The strong interaction what is the quantum of the strong interaction. The dependence of the cutoff wavenumber for shear waves on the coupling parameter is obtained. This paper is a didactic exploration of the physical rationale for.
Approximate analytical solutions of thedirac equation. Eigensolutions of the schrodinger equation with a class of yukawa. Derivation of the wave equation in these notes we apply newtons law to an elastic string, concluding that small amplitude transverse vibrations of the string obey the wave equation. The wave dispersion relations in the fluid phase of yukawa systems are obtained from molecular dynamics md simulations for a wide range of the parameters. The wave equation outline of mechanical waves longitudinal and transverse waves waves in a string, sound waves the wave equation description of waves using functions of two variables travelling waves the wave equation 0 y v y 1 2 2 2 2 2 x t waves in a string.
The relativistic wave equation is set up to describe the behavior of successive interelementary. Traveling wave solutions of the ndimensional coupled. In summary, we have shown that by solving the schrodinger equation 1. Yukawa potential 715 has also received a great deal of attention in view of the methods by which the potential has been studied. Out of equilibrium twodimensional yukawa theory in a strong. Thus, solving the dirac equation is very significant in describing the nuclear shell structure 19, 20. We discuss traveling wave solutions to the yukawa equations, a system of nonlinear partial differential equations which has applications to mesonnucleon interactions. Research article exact solution of the dirac equation for the. Almost everything we know about nuclear and atomic physics has been discovered by scattering experiments, e.
The yukawa equations are converted to a sixdimensional dynamical system, which is then studied for various values of the wave speed and mass parameter. Pdf radial solutions of the schrodingers equation with. According to the general principle of quantum theory, the field u is. The role of yukawa potential on the spin and pseudospin symmetry solution is investigated systematically by solving the dirac equation with attractive scalar sr and repulsive vector vr potentials.
Derivation of relativistic wave equations in the theory of elementary domains, progress of. Hideki yukawa and the pi mesons san jose state university. Semenov1,4 1moscow institute of physics and technology, 141700, dolgoprudny, russia. The first way is the variational method used by huithen and. By inserting yukawa potential to schrodinger equation, we investigated the behaviour of microscopic particle in the nonrelativistic quantum system by calculating. The solutions of the one wave equations will be discussed in the next section, using characteristic lines ct. Thomas2 1aixmarseilleuniversite, cnrs, laboratoire piim, umr 7345, 397 marseille cedex 20, france. The word classical is here used in the sense not quantum mechanical. Traveling wave solutions of the ndimensional coupled yukawa. Semenov1,4 1moscow institute of physics and technology, 141700, dolgoprudny, russia 2institute for theoretical and experimental physics, 117218, moscow, russia. This decomposition is used to derive the classical dalembert solution to the wave equation on the domain. The bound state energy eigenvalues and the corresponding unnormalized eigenfunctions are obtained in terms of the laguerre polynomials. Approximate analytical solutions of the perturbed yukawa potential.
Approximate solution to the schrodinger equation with. Closed forms of the energy eigenvalue equations and the spinor wave functions are computed by using the nikiforovuvarov method. We relate it to earlier discussions on an oscillator model for the nucleus. Approximate solution to the schrodinger equation with manning. An integral equation for distorted wave amplitudes pdf free. Hideki yukawa received the nobel prize in physics for 1949 for predicting the existence of what became to be known as the pi mesons and later as pionsin his 1934 article yukawa argued that the nuclear strong force is carried by a particle with a mass approximately 200 times that of an electron.
Yukawa potential and the propagator term consider the electrostatic potential about a charged point particle. Chapter 4 the wave equation another classical example of a hyperbolic pde is a wave equation. Finally, we give a brief discussion in section4before the conclusion in section5. Research article exact solution of the dirac equation for. Eigensolutions of the schrodinger equation with some physical. Proca equation is a relativistic wave equation for a massive spin1 particle. Some of them used to solving the wave equations are the 1nexpansion 16 and shifted 1nexpansion methods 17, studying the potential by using the. We make kleingordon equation is satisfied by yukawa potential 4dimensional wave equation of yukawa wave function. By considering the e ects of pertubative interaction potential, we see that the. We expand this potential around of its mesonic cloud that gets a new form with great powers and inverse exponent. The strong interaction rensselaer polytechnic institute. Assuming that the spacetime consists of elementary domains proposed by yukawa, we attempt to extend the stochastic quantization procedures introduce.
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