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I am doing research in the field of number theory and as part of this looking for correspondencies to other discilines and particularly physics. I am searching for examples in physics where the equation below finds its application: $$\frac{\partial^2\psi}{\partial x^2}=\psi(x)+ x \frac{\partial\psi}{\partial x} \qquad (*)$$

under the constraint $$\Psi(x)=\sum_{k=-j}^j \psi(x,k,j)=\sum_{k=-j}^j \frac{2 \pi}{j}\,e^{(i\,2\pi\,(k-1)\,x / j)}$$

Particularly inetresting also whether this equation $(*)$ comes in other notations such as in classical quantum mechanics. Please see this as a research type of question rather solving a mathematical problem.

I would really appreciat your help.

Thanks a lot

PS: although this question relates to Number theoretical function applied in physics? but it is not the same, here it is really about the differential equation.

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closed as not constructive by dmckee May 30 '13 at 14:47

As it currently stands, this question is not a good fit for our Q&A format. We expect answers to be supported by facts, references, or expertise, but this question will likely solicit debate, arguments, polling, or extended discussion. If you feel that this question can be improved and possibly reopened, visit the help center for guidance.If this question can be reworded to fit the rules in the help center, please edit the question.

Welcome, to Physics.SE, al-Hwarizmi. As with most Stack Exchange site, we consider questions of the form "lets build a list of [something]" to be poor fits to the question and answer model we use here, and discourage them. – dmckee May 30 '13 at 14:50