Abstract
Consider
Let us recall the situation for α = 0:
Without taking into account the boundary condition at 0, the eigenfunctions are
where the H m (x) are Hermite polynomials. Because of the boundary condition φ(0) = 0 only odd m (= 2n + 1) are allowed:
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Notes and references
A.M. Perelomov; Theor. Math. Phys. 6 (1971) 263.
V. Bargmann; Annals of Math. Vol. 48 #3 (1947) 568.
I.S. Gradsteyn, I.M. Ryshik; Tables of Integrals, Series and Products, Academic Press 1965.
S. Helgason; Differential Geometry and Symmetric Spaces, Academic Press 1962.
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© 1992 Springer-Verlag Berlin Heidelberg
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(1992). Algebraic Approach to x 2 + α/x 2 Interactions. In: Lectures on Integrable Systems. Lecture Notes in Physics Monographs, vol 10. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-47274-2_4
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DOI: https://doi.org/10.1007/978-3-540-47274-2_4
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