The CWKB approach to non-reflecting potential and cosmological implications

Details The CWKB approach to non-reflecting potential and cosmological implications The CWKB approach to non-reflecting potential and cosmological implications

2002-07-02

arxiv.org/abs/gr-qc/0207015v1

Pramana62:1231-1240,2004

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

9 pages, latex

Scientific paper

10.1007/BF02704436

We discuss the method of calculating the reflection coefficient using complex trajectory WKB (CWKB) approximation. This enables us to give an interpretation of non-reflecting nature of the potential under certain conditions and clarify some points, reported incorrectly elsewhere [vs:ejp] for the potential $U(x)=-U_0cosh^2(x/a)$. We show that the repeated reflectios between the turning points are essential, which most authors overlooked, in obtaining the non-reflecting c ondition. We find that the considered repeated reflection paths are in conformity with Bogolubov transformation technique. We discuss the implications of the results when applied to the particle production scenario, considering $x$ as a time variable and also stress the cosmological implications of the result with reference to radiation domonated and de Sitter spacetime.

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