Phase-Integral Approximation of Arbitrary Order Generated from an Unspecified Base Function

作者: Nanny Fröman , Per Olof Fröman

DOI: 10.1007/978-1-4612-2342-9_1

关键词: Schrödinger equationMathematical analysisDifferential equationMathematicsSection (fiber bundle)A priori and a posterioriWKB approximationPhase (waves)Order (group theory)Invariant (mathematics)

摘要: We begin with a brief review of the so-called WKB approximation, its deficiencies in higher order, and attempts by several authors to remedy them. It is then shown that these do not appear phase-integral approximation generated from an priori unspecified base function, which was originally devised present 1974 presented here way clarifies role “small” parameter differential equation. The advantage this versus order also discussed. In discussion relations between solutions Schrodinger equation q-equation, Ermakov-Lewis invariant considered. concluding section we mention other items constitute method beside question.

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