Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1997-01-28
Nucl.Phys. B509 (1998) 529-555
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Few minor corrections
Scientific paper
10.1016/S0550-3213(97)00617-2
The necessary and sufficient conditions for the exactness of the semiclassical approximation for the solution of the Schr\"odinger and Klein-Gordon equations are obtained. It is shown that the existence of an exact semiclassical solution of the Schr\"odinger equation determines both the semiclassical wave function and the interaction potential uniquely up to the choice of the boundary conditions. This result also holds for the Klein-Gordon equation. Its implications for the solution of the Wheeler-DeWitt equation for the FRW scalar field minisuperspace models are discussed. In particular, exact semiclassical solutions of the Wheeler-DeWitt equation for the case of massless scalar field and exponential matter potentials are constructed. The existence of exact semiclassical solutions for polynomial matter potentials of the form $\lambda\phi^{2p}$ is also analyzed. It is shown that for p=1, 2 and 3, right-going semiclassical solutions do not exist. A generalized semiclassical perturbation expansion is also developed which is quite different from the traditional $\hbar$ and $M_p^{-1}$-expansions.
No associations
LandOfFree
Exact Semiclassical Evolutions in Relativistic and Nonrelativistic Scalar Quantum Mechanics and Quantum Cosmology does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Exact Semiclassical Evolutions in Relativistic and Nonrelativistic Scalar Quantum Mechanics and Quantum Cosmology, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Exact Semiclassical Evolutions in Relativistic and Nonrelativistic Scalar Quantum Mechanics and Quantum Cosmology will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-672667