JPS 2010 Autumn Meeting

12aSC-9
Solution for the New Grammar Version of Schrödinger Equation (2)
http://www.grammaticalphysics.ac/ / Yuichi Uda
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This time, I report a recent result of solving the equation proposed at JPS 2009 Autumn Meeting 13pSH-3 as a sequel to that presentation.
The following two advances were achieved after the previous meeting.
(1) I found a form of some solutions not only in the case where each of the solutions is a function of only the first pair of fourier coefficients but in the case where each of the solutions is a function of only the n-th pair of fourier coefficients.
(2) I wrote the expression of the form in terms of a Fourier integral instead of a power series expansion.
Concretely saying, the form of the solutions is as follows.

where f is a complex-valued function of a real variable which is not zero only when hr²/(2nπαm) is an integer and a_n[χ] is the n-th Fourier cosine coefficient and b_n[χ] is the n-th Fourier sine coefficient.

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Last edited at 2011/04/23/11:12JST