I have a question..I am trying to solve a differential equation that arises in my research problem. Because the differential equation has no solution in terms of well known functions, I had to construct a series solution for the differential equation which is physical and agrees with the potential energy of the system (potential energy minimum at a point,then wavefunctions maximum at that particular point). Anyhow the eigenvalues of the matrix arising from solving the series are energies but are sometimes complex which makes the solution non physical!! what can be done in this case? Changing the matrix into Hermitian by adding it to the Transpose and dividing by 2 is mathematical I guess and will not produce the correct values of energies..Can anyone help please. Thanks..(adsbygoogle = window.adsbygoogle || []).push({});

N.B: The differential equation is:

[tex] (1-x^2)~ \frac{\partial ^2 F(x,y)}{\partial x}+\left(\frac{1-2x^2}{x}\right)~\frac{\partial F(x,y)}{\partial x}-\left[ax^2(1-2y^2)-c\right] F(x,y)=0 [/tex]

where x and y are the variables and a and c are constants

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# Non Hermitian Hamiltonian!

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