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Semiclassical approximation to the partition function of a particle in D dimensions
de Carvalho CA1, Cavalcanti, Fraga
1Department of Physics and Astronomy, University of California, Los Angeles, California 90095-1547, USA.
Summary
This study derives a semiclassical approximation for particle partition functions in D dimensions using path integrals. It provides explicit formulas for potentials and compares specific heat calculations to WKB estimates.
Area of Science:
- Quantum mechanics
- Statistical mechanics
- Mathematical physics
Background:
- The partition function is crucial for understanding thermodynamic properties of quantum systems.
- Semiclassical methods offer approximations for complex quantum systems.
Purpose of the Study:
- To develop a semiclassical series for the partition function of a D-dimensional particle.
- To analyze attractive central potentials and derive explicit expressions for key quantities.
Main Methods:
- Utilizing a path integral formalism.
- Deriving a semiclassical series expansion.
- Calculating fluctuation determinants and semiclassical two-point functions.
Main Results:
- Obtained explicit expressions for the fluctuation determinant and semiclassical two-point function for harmonic and quartic anharmonic oscillators.
- Calculated the specific heat for the quartic anharmonic oscillator.
- Compared results with precise WKB estimates.
Conclusions:
- The derived semiclassical approach provides accurate approximations for quantum systems.
- The methods can potentially be extended to quantum field theories.