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I have solved the Schrödinger equation for a triangular well potential and the solution comes in terms of Airy functions...now i am facing the following problems: What are the normalization constants of Airy functions?

What are the asymptotic forms Airy functions?

How to find the matrix elements of the airy function?

If anybody knows the answer please tell me as soon as possible.

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closed as off-topic by j.c., Andrey Rekalo, Ramiro de la Vega, Cam McLeman, Carlo Beenakker Sep 24 '13 at 17:07

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This sounds like homework. You want to try over at Math or Physics Stack exchange, or Wikipedia. –  Ray Yang Feb 7 '13 at 9:06

3 Answers 3

You can go to the OLver book, Asymptotic and special functions, 1974, and find your answers.

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I recommend to look at pages 213-4-5 in the first volume of Hörmander's ALPDO, Springer Grundlehren, 256. In my opinion this is the shortest and most elementary introduction to Airy functions.

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The Airy function can be expressed in terms of a modified Bessel function of the 2nd kind; this amounts to Exercise 20, Ch. IV of Andrews, Askey and Roy's red book on special functions (for which the authors refer the reader to Watson's 1944 treatise on Bessel functions), and an asymptotic formula for modified Bessel functions of the 1st and 2nd kind is given on p. 223 (ed. 1999).

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