Suppose our aim is to find out the interaction energy between the two particles like electron - electron (Same conduction band) and hole - hole (Same valance band) in a low dimensional systems. Is it correct to reduce this as one particle using reduced mass and then solve the Schrodinger equation for finding the interaction energy if we want to mainly focus on the interaction alone and how this differs from the case if we consider the electron(conduction band) - hole (Valence band) interaction? Can anyone give me the brief detail about this please?
Dear P. Kalpana
Regards
If you are interested only in two body interaction with a radial potential is possible solved the schrödinger equation for the two particles. There are several techniques such as variational procedures or by direct integration by mean of numerical techniques. When you considered the two particles inside a structures the methods for solution can be different, DFT is a good option. The effective mass approach have obtaine good results for both bulk and nanostructures systems, (The_Physics_Of_Low-Dimensional_Semiconductors_An_Introduction_-_John_H._Davies).
Hope this helps, too.
If the reduced mass approach does not work for you then you may want to consider introducing relativity and spin into Schrodinger equation as discussed in the following article.
Article Quarkonium and hydrogen spectra with spin-dependent relativi...
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