2010-01-25 17:50:47 +08:00
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!
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2010-01-25 18:06:35 +08:00
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! Copyright (C) 2010 Quantum ESPRESSO group
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2010-01-25 17:50:47 +08:00
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! This file is distributed under the terms of the
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! GNU General Public License. See the file `License'
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! in the root directory of the present distribution,
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! or http://www.gnu.org/copyleft/gpl.txt .
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!
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!---------------------------------------------------------------
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subroutine start_scheq(lam,e,b,grid,ze2,y)
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!---------------------------------------------------------------
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!
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! determines the wave-function in the first two points by
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! series developement. It receives as input:
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! lam the angular momentum
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! e the energy in Ry
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! b(0:3) the coefficients of a polynomial that interpolates the
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! potential in the first three points
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! grid the mesh
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! ze2 the zed of the mesh
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! in output y(1:2) contains the solution in the first two points
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!
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USE kinds, ONLY : DP
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USE radial_grids, ONLY : radial_grid_type
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IMPLICIT NONE
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TYPE(radial_grid_type), INTENT(IN) :: grid
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INTEGER, INTENT(IN) :: lam
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REAL(DP), INTENT(IN) :: b(0:3), e
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REAL(DP) :: ze2, xl1, x4l6, x6l12, x8l20, b0e, c1, c2, c3, c4, rr1, rr2
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REAL(DP) :: y(1:2)
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INTEGER :: l1
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!
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! set up constants and initialize
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!
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l1=lam+1
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xl1=lam+1.0_DP
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x4l6=4.0_dp*lam+6.0_dp
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x6l12=6.0_dp*lam+12.0_dp
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x8l20=8.0_dp*lam+20.0_dp
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!
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!
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b0e=b(0)-e
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c1=0.5_dp*ze2/xl1
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c2=(c1*ze2+b0e)/x4l6
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c3=(c2*ze2+c1*b0e+b(1))/x6l12
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c4=(c3*ze2+c2*b0e+c1*b(1)+b(2))/x8l20
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rr1=(1.0_dp+grid%r(1)*(c1+grid%r(1)*(c2+grid%r(1)*(c3+grid%r(1)*c4))))*grid%r(1)**l1
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rr2=(1.0_dp+grid%r(2)*(c1+grid%r(2)*(c2+grid%r(2)*(c3+grid%r(2)*c4))))*grid%r(2)**l1
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y(1)=rr1/grid%sqr(1)
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y(2)=rr2/grid%sqr(2)
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return
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end subroutine start_scheq
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