Class of solutions of the Wheeler-DeWitt equation with ordering parameter
H. S. Vieira, V. B. Bezerra, C. R. Muniz, M. S. Cunha, H. R. Christiansen
Abstract
In this letter, we discuss the Wheeler-DeWitt equation with an ordering parameter in the Friedmann-Robertson-Walker universe. The solutions when the universe was very small and at the end of the expansion are obtained in terms of Bessel and Heun functions, respectively. We also obtain a boundary condition which should be satisfied by the ordering parameter, namely, 0≤p≤2. We investigate the minimum value of the scale factor with respect to the maximum value of the probability density.
Topics & Concepts
Bessel functionBoundary value problemMathematicsScale factor (cosmology)UniverseMathematical physicsClass (philosophy)Value (mathematics)Metric expansion of spaceApplied mathematicsPhysicsMathematical analysisStatisticsCosmologyQuantum mechanicsComputer scienceArtificial intelligenceDark energyCosmology and Gravitation TheoriesStatistical Mechanics and EntropyAdvanced Thermodynamics and Statistical Mechanics