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
Log In. Sign up to receive regular email alerts from Physical Review A. Journal: Phys. X Rev.
A Phys. B Phys. C Phys. D Phys. E Phys.
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.
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.
- Schaums Outline of Theory and Problems of Logic-.
- mathematics and statistics online.
- In the City: A Celebration of London Music.
- Upcoming Events?
- Plans For Wind Generator-Pt250-Blade-Plan10A!
- Schaums outline of theory and problems of continuum mechanics;
The first equation implies the second, but the converse isn't true. Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered.
- In the Beginning: Fundamentalism, the Scopes Trial, and the Making of the Antievolution Movement (H. Eugene and Lillian Youngs Lehman Series);
- From the Act of Judging to the Sentence: The Problem of Truth Bearers from Bolzano to Tarski: 328 (Synthese Library).
- On Practice and Contradiction.
- American Ghosts and Old World Wonders!
- The Dirac Equation and Its Solutions pdf - Web Education.
Is the Dirac equation equivalent to the Klein-Gordon equation for its left handed component? Ask Question.
- feyncalc - Solving the Dirac equation in an arbitrary metric - Mathematica Stack Exchange?
- Business Ecosystems: Constructs, Configurations, and the Nurturing Process;
Asked 4 years, 1 month ago.