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Classic and Quantum Motions of Scalar Particle in Beltrami-de Sitter Spacetime

From a five-dimensional Minkowski view the five-dimensional angular momentum of a free spin-0 particle moving in de Sitter spacetime is conservative, by which its timelike geodesics can be labeled completely and uniquely. Based on that observation and working in Beltrami coordinate for de Sitter spacetime, solutions and their asymptotic behavior to the Beltrami-de Sitter–Klein–Gordon equation are given.