Appendix B: Effective‐Mass Approximated Equation
Yoshimasa Murayama · 2001
Starting from the following Schrodinger equation:where VO is the potential of the regular lattice and AV is a deviation from VO of the actual potential of this problem.Now, let us expand such that where $k is the Bloch function, R the coordinate of is the Wannier function which is localized around R .function is defined by and x into a series of Bloch states, atom positions, and W ( T -R) It is obvious that the Wannier As Bloch states constitute an orthonormal set with respect to k, it is easy to show that Wannier functions do the same with respect to R.After a simple manipulation, we obtainHere E ( k ) appeared as the eigenenergy of the following equation: Mesoscopic Systems: Fundamentals and Applications