Bessel.py

""" From "COMPUTATIONAL PHYSICS" & "COMPUTER PROBLEMS in PHYSICS"
    by RH Landau, MJ Paez, and CC Bordeianu (deceased)
    Copyright R Landau, Oregon State Unv, MJ Paez, Univ Antioquia, 
    C Bordeianu, Univ Bucharest, 2017. 
    Please respect copyright & acknowledge our work."""

# Bessel.py
from visual import *
from visual.graph import *

Xmax = 40.
Xmin = 0.25
step = 0.1                                       # Global class variables
order = 10; start = 50        # Plot j_order
graph1 = gdisplay(width = 500, height = 500, title = 'Sperical Bessel, \
       L = 1 (red), 10',xtitle = 'x', ytitle = 'j(x)',\
			 xmin=Xmin,xmax=Xmax,ymin=-0.2,ymax=0.5)
funct1 = gcurve(color=color.red)
funct2 = gcurve(color=color.green)
def down (x, n, m):                        # Method down, recurs downward
     j = zeros( (start  +  2), float)
     j[m  +  1] = j[m] = 1.                         # Start with anything
     for k in range(m, 0,  - 1):
         j[k - 1] = ( (2.*k + 1.)/x)*j[k]  -  j[k + 1]
     scale = (sin(x)/x)/j[0]               # Scale solution to known j[0]
     return j[n] * scale

for x in arange(Xmin, Xmax, step):
    funct1.plot(pos = (x, down(x, order, start)))
    
for x in arange(Xmin, Xmax, step):
    funct2.plot(pos = (x, down(x,1,start)))