### comsol

#### COMSOL Schrödinger Equation

I want to solve the Schrödinger equation in COMSOL with some specified boundary conditions. As an ODE the schrödinger equations reads (in 1D): af''(x) + b(x)f(x) = Ef(x), where E is an unknown constant that will be determined by the boundary conditions. I am not used to using COMSOL so I don't know if it is possible to solve this problem. So far all the templates for solving differential equations contains some generic form, where you have to specify the value of the constants before each term. This does not work for the eigenvalue problem above, where E is unknown. Does anyone know how to specify the differential equation as an eigenvalue equation, where E is unknown?

I have been conducting research in the area of quantum dots and rings for over 7 years and here is what I would do. Choose the PDE interfaces under the Mathematical models. Then pick the Coefficient Form PDE(c). Then choose from the Preset Studies: Eigenvalue. Set e, f, and alpha, beta, and gamma to zero. The coefficients a and c cant be set once you know the scale of the system. When you run the simulation, it will give you the value for lambda which is the eigenvalue and corresponds to E.

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