Klein-Gordon-Schrodinger and Dirac equations

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In summary, the conversation discusses the need to solve the Klein-Gordon-Schrodinger and Dirac equations for the Coulombian potential. The equations are given, but the potential term needs to be added. The attempt at a solution involves referencing a book for solving both equations for the Coulomb potential, but the person does not have access to the book.
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Lecticia
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Homework Statement


I need to solve the Klein-Gordon-Schrodinger and the Dirac equation for the Coulombian potential.

Homework Equations



KGS:
[tex][(\partial^{\mu}\partial_{\mu} + m^2c^2/h^2)\Psi=0 [/tex]
I don't know how I can add the potential term...

Dirac:
[tex][\gamma^{\mu}(ih\partial_{\mu} - (e/c) A_{\mu})-mc)]\Psi=0 [/tex]

The Attempt at a Solution



I'm trying to do something with these equations in order to make them with a Schrodinger-like form. For the Dirac eq., I found the hydrogen atom resolved in Sakurai's book, but I could not understand what they did (they took about 10 pages) and I wonder if there is another (easier) way to do this.
 
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There really isn't anu other way. A book solving both equations for the Coulomb potential is Greiner's "Relativistic Quantum Mechanics - Wave equations".
 
  • #3
dextercioby said:
There really isn't anu other way. A book solving both equations for the Coulomb potential is Greiner's "Relativistic Quantum Mechanics - Wave equations".

Thanks. I'll look for this book online, 'cos I don't have it... :(
 

What is the significance of the Klein-Gordon-Schrodinger and Dirac equations in physics?

The Klein-Gordon-Schrodinger and Dirac equations are fundamental equations in quantum mechanics that describe the behavior of particles at the subatomic level. They are used to study the properties of particles such as electrons, protons, and neutrons, and have been crucial in developing our understanding of the behavior of matter and energy.

What is the difference between the Klein-Gordon-Schrodinger and Dirac equations?

The Klein-Gordon and Schrodinger equations are both wave equations that describe the behavior of particles in quantum mechanics. However, the Dirac equation is a more comprehensive equation that takes into account the relativistic effects of particles moving at high speeds. It also predicts the existence of antimatter, a concept that was later confirmed by experiments.

How do the Klein-Gordon-Schrodinger and Dirac equations relate to each other?

The Klein-Gordon-Schrodinger equation is a combination of the Klein-Gordon and Schrodinger equations, and it is used to describe particles with spin 0 or 1. On the other hand, the Dirac equation is a more general form that is used to describe particles with spin 1/2. Both equations are essential in understanding the behavior of particles in quantum mechanics.

What are the applications of the Klein-Gordon-Schrodinger and Dirac equations?

The Klein-Gordon-Schrodinger and Dirac equations have numerous applications in physics, including studying the properties of atoms, molecules, and nuclei. They are also used in quantum field theory to study the interactions of particles and fields. In addition, these equations play a crucial role in developing technologies such as transistors and lasers.

What are some of the challenges in solving the Klein-Gordon-Schrodinger and Dirac equations?

One of the main challenges in solving these equations is that they are nonlinear equations, which makes it difficult to find exact solutions. In addition, the equations are often coupled with other equations, making it even more challenging to find solutions. As a result, numerical methods are often used to approximate solutions to these equations.

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