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A product formula for the eigenfunctions of a quartic oscillator
We consider the Schrödinger operator on the real line with an even quartic potential. Our main result is a product formula of the type. ψk(x)ψk(y)=∫Rψk(z)K(x,y,z)dz for its eigenfunctions ψk. The kernel function K is given explicitly in terms of the Airy function Ai(x), and it is positive for approp...
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| Main Authors: | , |
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| Format: | Default Article |
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2015
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| Online Access: | https://hdl.handle.net/2134/17028 |
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| _version_ | 1818173024386416640 |
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| author | Martin Hallnas Edwin Langmann |
| author_facet | Martin Hallnas Edwin Langmann |
| author_sort | Martin Hallnas (1248081) |
| collection | Figshare |
| description | We consider the Schrödinger operator on the real line with an even quartic potential. Our main result is a product formula of the type. ψk(x)ψk(y)=∫Rψk(z)K(x,y,z)dz for its eigenfunctions ψk. The kernel function K is given explicitly in terms of the Airy function Ai(x), and it is positive for appropriate parameter values. As an application, we obtain a particular asymptotic expansion of the eigenfunctions ψk. |
| format | Default Article |
| id | rr-article-9384950 |
| institution | Loughborough University |
| publishDate | 2015 |
| record_format | Figshare |
| spelling | rr-article-93849502015-01-01T00:00:00Z A product formula for the eigenfunctions of a quartic oscillator Martin Hallnas (1248081) Edwin Langmann (7160933) Other mathematical sciences not elsewhere classified Asymptotic expansions Kernel functions Product formula Quartic oscillator Mathematical Sciences not elsewhere classified We consider the Schrödinger operator on the real line with an even quartic potential. Our main result is a product formula of the type. ψk(x)ψk(y)=∫Rψk(z)K(x,y,z)dz for its eigenfunctions ψk. The kernel function K is given explicitly in terms of the Airy function Ai(x), and it is positive for appropriate parameter values. As an application, we obtain a particular asymptotic expansion of the eigenfunctions ψk. 2015-01-01T00:00:00Z Text Journal contribution 2134/17028 https://figshare.com/articles/journal_contribution/A_product_formula_for_the_eigenfunctions_of_a_quartic_oscillator/9384950 CC BY-NC-ND 4.0 |
| spellingShingle | Other mathematical sciences not elsewhere classified Asymptotic expansions Kernel functions Product formula Quartic oscillator Mathematical Sciences not elsewhere classified Martin Hallnas Edwin Langmann A product formula for the eigenfunctions of a quartic oscillator |
| title | A product formula for the eigenfunctions of a quartic oscillator |
| title_full | A product formula for the eigenfunctions of a quartic oscillator |
| title_fullStr | A product formula for the eigenfunctions of a quartic oscillator |
| title_full_unstemmed | A product formula for the eigenfunctions of a quartic oscillator |
| title_short | A product formula for the eigenfunctions of a quartic oscillator |
| title_sort | product formula for the eigenfunctions of a quartic oscillator |
| topic | Other mathematical sciences not elsewhere classified Asymptotic expansions Kernel functions Product formula Quartic oscillator Mathematical Sciences not elsewhere classified |
| url | https://hdl.handle.net/2134/17028 |