
from sympy import symbols, I, sin, pi, diff, exp
from sympy import simplify

r, theta, phi = symbols('r theta phi')

# Define the function u(theta, phi)
u = - (3 / (8 * pi))**(1 / 2) * exp(I * phi) * sin(theta)

# Apply the Laplacian
laplacian_u = 1 / (r**2 * sin(theta)) * diff(sin(theta) * diff(u, theta), theta) + 1 / (r**2 * sin(theta)**2) * diff(u, phi, 2)

# Simplify the result
simplified_laplacian_u = simplify(laplacian_u)

# Compute 'c'
c = simplify(simplified_laplacian_u / u)
print(c)
