New explicit nonperiodic solutions of the homogeneous wave equation |
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Authors: | Héctor A. Múnera Octavio Guzmán |
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Affiliation: | (1) Centro International de Física, A.A. 251955, Bogotá D.C., Columbia, South America;(2) Departmento de Física, Universidad Nacional, Bogota D.C., Columbia, South America |
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Abstract: | We exhibit a newansatz for the solution of the homogeneous three-dimensional time-dependent wave equation in spherical coordinates of the form Φ(r,t)=Y(θ, φ)(I(r)+G(g)), whereg ≡ct/r. FunctionG(g) has explicit solution in terms of three independent nonperiodic functionss ℓ,t ℓ,u ℓ (s ℓ andt ℓ are related to the associated Legendre functions of the first and second kinds).G(g) is nonperiodic and may be cast as a superposition of incoming and outgoing waves. To obtainG(g), we solved a nonhomogeneous associated Legendre equation (this solution, to our knowledge, is also new).G(g) may prove useful in many microscopic and macroscopic problems, representable by homogeneous wave equations. |
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Keywords: | homogeneous wave equation three-dimensional spherical travelling waves nonperiodic closed d’ Alembertian solutions time-independent components nonhomogeneous associated Legendre functions incoming/outgoing waves |
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