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Application of the trace formula in pseudointegrable systems
Stefanie Russ1, Jesper Mellenthin
1Institut für Theoretische Physik III, Justus-Liebig-Universität Giessen, D-35392 Giessen, Germany.
Summary
Periodic-orbit theory accurately calculates quantum mechanical eigenvalues for polygon and barrier billiards. This method provides precise results for the first 100 eigenvalues, matching Schrödinger equation solutions.
Area of Science:
- Quantum mechanics
- Mathematical physics
Background:
- Pseudointegrable billiards present challenges in quantum eigenvalue calculations.
- Periodic-orbit theory offers a potential avenue for simplifying these calculations.
Purpose of the Study:
- To apply periodic-orbit theory to calculate the integrated density of states N(k) for polygon and barrier billiards.
- To validate the accuracy of periodic-orbit calculations against numerical solutions of the Schrödinger equation.
Main Methods:
- Utilizing periodic-orbit theory to compute the integrated density of states.
- Performing numerical solutions of the Schrödinger equation for comparison.
Main Results:
- Periodic-orbit theory calculations show strong agreement with numerical results.
- Accurate determination of approximately the first 100 quantum mechanical eigenvalues is achieved.
Conclusions:
- Periodic-orbit theory is a reliable and accurate method for calculating quantum eigenvalues in pseudointegrable billiards.
- This approach offers a direct and efficient way to obtain a significant number of eigenvalues.
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