Single particle approximation for a conduction band electron?
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I have a problem which on some levels appears very simple, but others quite complex so I thought I'd ask here to make sure I am on the right track before going ahead any further
I have a 3D potential well with a single electron in it. I know the functional form of the potential in all 3 dimensions, and so I'd like to calculate the PDF of the electron so I can get an effective "volume" for the electron by using a cut-off value of the PDF and integrating in 3 dimensions.
The potential well itself is in a silicon device, and the electron is within the conduction band by itself. Is it adequate to treat the electron as a single particle in this instance with no interference from the lattice? Are there any additional considerations I need before I simply substitute in the potential and try and solve (which i will probably do numerically...) ?
Thanks
I have a 3D potential well with a single electron in it. I know the functional form of the potential in all 3 dimensions, and so I'd like to calculate the PDF of the electron so I can get an effective "volume" for the electron by using a cut-off value of the PDF and integrating in 3 dimensions.
The potential well itself is in a silicon device, and the electron is within the conduction band by itself. Is it adequate to treat the electron as a single particle in this instance with no interference from the lattice? Are there any additional considerations I need before I simply substitute in the potential and try and solve (which i will probably do numerically...) ?
Thanks
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