- #1
d4n1el
- 3
- 1
Hi!
Im trying to do some rather easy QM-calculations in Fortran.
To do that i need a routine that calculates the generalized Laguerre polynomials.
I just did the simplest implementation of the equation:
[tex]L^l_n(x)=\sum_{k=0}^n\frac{(n+l)!(-x^2)^k}{(n-k)!k!}[/tex]
I implemented this in the following way:
The code is running and i do get results, but when i compare them with the results given in for example Mathematica, they seems quite strange.
So my questions are: Do you see some obvious mistakes? Do you think there are possibilities for numerical errors? (In such a case, do you have any advices on improvments?)
When i have been googling around, it looks like a lot of the numerical implementations are using recursive relations. What are the pro's and con's for doing this kind of calculation in such a manner?
Im trying to do some rather easy QM-calculations in Fortran.
To do that i need a routine that calculates the generalized Laguerre polynomials.
I just did the simplest implementation of the equation:
[tex]L^l_n(x)=\sum_{k=0}^n\frac{(n+l)!(-x^2)^k}{(n-k)!k!}[/tex]
I implemented this in the following way:
Code:
SUBROUTINE LAGUERRE(n,l,r,u,arraylength)
Implicit none
INTEGER, INTENT(IN) :: arraylength,n
real(kind=kind(0.d0)), INTENT(IN) :: l
REAL(kind=kind(0.d0)), INTENT(IN),DIMENSION(arraylength) :: r
REAL(kind=kind(0.d0)), INTENT(OUT),DIMENSION(arraylength) :: u
REAL(kind=kind(0.d0)), DIMENSION(arraylength) :: temp
Integer :: m
temp=0.d0
do m=0,n
temp=temp+gamma(real(n)+l+1.0)*(-r)**m/
+ (gamma(real(n)-real(m)+1.0)*gamma(l+real(m)+1.0)
+ *gamma(real(m)+1.0))
end do
u=temp
END SUBROUTINE LAGUERRE
The code is running and i do get results, but when i compare them with the results given in for example Mathematica, they seems quite strange.
So my questions are: Do you see some obvious mistakes? Do you think there are possibilities for numerical errors? (In such a case, do you have any advices on improvments?)
When i have been googling around, it looks like a lot of the numerical implementations are using recursive relations. What are the pro's and con's for doing this kind of calculation in such a manner?