Non-radial stellar oscillations: A perspective from potential scattering 1: Theoretical foundations

Computer Science – Sound

Scientific paper

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Brunt-Vaisala Frequency, Cavity Resonators, Perturbation, Potential Fields, Regge Poles, Sound Waves, Stellar Models, Stellar Oscillations, Wave Scattering, Bessel Functions, Eigenvalues, Matrices (Mathematics), Phase Shift, Quantum Mechanics, Schroedinger Equation, Solar Interior, Sturm-Liouville Theory

Scientific paper

This article is the first in a series designed to gain insight into the stellar oscillation problem from a somewhat novel point of view: that of potential scattering, well-known in the quantum mechanical literature. In this paper the known theoretical foundations are developed and applied in the context of the astrophysical problem, wherein the star itself (rather than any portion of it) is the potential which 'scatters' waves and 'traps' them. The basis for the identification of a precisely defined scattering problem is the existence of a linear Schroedinger equation associated both globally and locally with the nonlinear eigenvalue equation for non-radial stellar pulsations. The paper is also designed to be a fairly complete account of the relevant mathematical topics that are germane to a study of this kind.

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