# Read e-book The Dirac Equation and Its Solutions

Using the first of these, then a single equation for can be obtained. Since , the equation is only satisfied if the quantity in the brackets vanishes, which yields the eigenvalues.

We see that the eigenvalues can be positive or negative. A plot of the energy levels is shown below:. There is a continuum for turquoise and for periwinkle. There is also a gap between and. We will show that for , an appropriate solution is to take. Note that when , the third and fourth components of vanish. Authorization Required.

## Free The Dirac Equation And Its Solutions

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Perhaps after quantizing? If so how do they differ? EDIT: To put what I'm saying in other words: Is the field theory of a Dirac spinor obeying the Dirac equation equivalent to the field theory of a left handed spinor obeying the KG equation? The Dirac equation is more restrictive than the Klein-Gordon equation.

L4.4 Dirac equation for the electron and hydrogen Hamiltonian

For every solution to the Dirac equation, its components will be a solution of the Klein-Gordon equation, but the converse isn't true: if you form a spinor whose components are solutions of the Klein-Gordon equation, it might not solve the Dirac equation. But, what happens if we plug these solutions in the original Dirac equation?

## The Dirac Equation and Its Solutions pdf

If you consider only the Klein-Gordon equation, you're introducing extra "solutions" that don't really solve the Dirac equation. Why does this happen? You can regard the Klein-Gordon equation as the "squared" version of the Dirac equation. And when you square an equation, you always get this nasty false solutions: if you have e.

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