[Pw_forum] Transmission calculation using PWCOND

[Manoj Srivastava]

Dear PWSCF users and developers,
 I have been trying to understand the PWCOND code for transmission
calculation, basically 'transmit.f90' file. The wavefunction in the left
lead, right lead and scattering region is given by - 
  
       psi_k+sum_{k'}r_{kk'}psi_k'
  psi= sum_{n} a_n psi_n+ sum_{\alpha l m} C_{\alpha l m}psi_{\alpha l m}
       sum_{k'}t_{kk'}psi_k'

The above expression is from Choi & Ihm's paper, on which I believe PWCOND
is based on. Now undetermined coefficients in above expression are
r_{kk'}, a_n, C_{\alpha,l,m}, t_kk'. I am confused on code evaluates these
coefficients.  My understanding is you first get the wavefunction in the
leads and then solve scattering region the same way to get the
wavefunction in scattering region, so at this point you have already
determined a_n and C_{\alpha,l,m}. At last do boundary matching condition
between leads and scattering region to get reflection and transmission
coefficient. Am I right? My thinking is based on simple quantum mechanics
scattering problem where we solve schrodinger's equation in each region
and then do boundary matching to get reflection and transmission
coefficients.

Now looking at the subroutine 'transmit.f90', this does not appear to be
the case. It seems as if we are solving the Schrodinger's equation in the
scattering region and doing boundary matching at the same time. Using a
big matrix and solving something like AX=B. Would anybody mind explaing
what's going on in subroutine transmit.f90? 

Regards, 
Manoj Srivastava 
Physics Graduate Student 
University Of Florida, Gainesville, FL