Nugroho's blog.: Even Wave Equation on Infinite-depth Potential Well (with Some Variation Potential in Between) using Shooting Method,

Wednesday, March 30, 2016

Even Wave Equation on Infinite-depth Potential Well (with Some Variation Potential in Between) using Shooting Method,

It's from previous code, I use it to simulate even function.


from pylab import *

figure(3)
n = 39
psi0= zeros(n) #
psi = psi0 #
x = linspace(0,1,n)
V = zeros(n)
#V = 39*pow(x,2)

for i in arange(n):
if i<n/2.:
V[i] = 73.
else:
V[i] = 0.

psi0[0] = 1.
psi0[1] = psi0[0] #for odd function, use another value, 
                  #but psi0[0] must be zero

t = 0
dx = 1./n
E = 1.
dE = .1
err = .05
while t< 771:
#k = 2*dx*dx*(E-V)
for i in range (1,n-1):
k = 2*dx*dx*(E-V[i])
psi[i+1] = 2*psi0[i]-psi0[i-1]-k*psi0[i]
psi0 = psi
if abs(psi[n-1])<err:
print E
plot(x,psi)
t += 1
E += dE

xlabel('x')
ylabel('psi')
title('Fungsi Gelombang')
grid(True)
savefig("shooting.png")

figure(2)
plot(x,V)

xlabel('x')
ylabel('V')
title('Potensial')
grid(True)

show()



.
Here's some result with different potential V









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