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def find_analytic_energies(en):
    """
    Calculates Energy values for the finite square well using analytical
    model (Griffiths, Introduction to Quantum Mechanics, page 62.)
    """
    z = sqrt(2*en)
    z0 = sqrt(2*Vo)
    z_zeroes = []
    f_sym = lambda z: tan(z)-sqrt((z0/z)**2-1)      # Formula 2.138, symmetrical case
    f_asym = lambda z: -1/tan(z)-sqrt((z0/z)**2-1)  # Formula 2.138, antisymmetrical case
    # first find the zeroes for the symmetrical case
    s = sign(f_sym(z))
    for i in range(len(s)-1):   # find zeroes of this crazy function
       if s[i]+s[i+1] == 0:
           zero = brentq(f_sym, z[i], z[i+1])
           z_zeroes.append(zero)
    print "Energies from the analytical model are: "
    print "Symmetrical case)"
    for i in range(0, len(z_zeroes),2):   # discard z=(2n-1)pi/2 solutions cause that's where tan(z) is discontinuous
        print "%.4f" %(z_zeroes[i]**2/2)
    # Now for the asymmetrical
    z_zeroes = []
    s = sign(f_asym(z))
    for i in range(len(s)-1):   # find zeroes of this crazy function
       if s[i]+s[i+1] == 0:
           zero = brentq(f_asym, z[i], z[i+1])
           z_zeroes.append(zero)
    print "(Antisymmetrical case)"
    for i in range(0, len(z_zeroes),2):   # discard z=npi solutions cause that's where cot(z) is discontinuous
        print "%.4f" %(z_zeroes[i]**2/2)