Take the 2-minute tour ×  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.
share|improve this question  closed as not constructive by
dmckee May 30 '13 at 14:47   Welcome, to Physics.SE, al-
Hwarizmi. As w