html('<h3>Quantum tetrahedron Volume Eigenvalue</h3>')

html('Enter the four J values into the input boxes')

html('k values k ranges from kmin to kmax in integer steps')

html('The dimension d of the Hilbert space H4,  d = kmax - kmin + 1')

html('kmin = max(|j1-j2|,|j3 -j4|) kmax = min(j1+j2,j3 +j4)')

html('The the dimension of the hilbert space is given by d = kmax -kmin + 1') 

html('V^2 =M = 2/9(real antisymmetrix matrix))')

html('Spins must satisfy (j1+j2)<= (j3+j4)')

html('Reference: Bohr-Sommerfeld Quantization of Space by Eugenio Bianchi and Hal M. Haggard ')

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import numpy

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@interact

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def _(j1 = input_box(6.0, 'J1'),

      j2= input_box(6.0, 'J2'),

      j3= input_box(6.0, 'J3'),

      j4= input_box(7.0, 'J1'), auto_update=False):

    if (j1+j2)<= (j3+j4):

        html('<h3>Values of Volume Eigenvalue</h3>')

        kmin = int(max(abs(j1-j2),abs(j3 -j4)))

        kmax = int(min((j1+j2),(j3 +j4)))

        d = kmax -kmin + 1

        y=numpy.arange(kmin,kmax+1,1)

        kmatrix = matrix(CDF,int(d), int(d))

        r=list()

        for j in range(d):

            k=int(y[j])

            c1 = -i*k

            c2 = sqrt(4*k*k - 1)

            c3 = sqrt(j1*(j1+1))

            c4 = sqrt((2*j1+1))

            c5 = sqrt(j3*(j3+1))

            c6 = sqrt((2*j3+1))

            c7 = wigner_6j(j1,1,j1,k,j2,k-1)

            c8 = wigner_6j(j3,1,j3,k,j4,k-1)

            a = c1*c2*c3*c4*c5*c6*c7*c8

            r.append(a)

            q=numerical_approx(a, digits=10)

            #print r

        for j in range(d-1):

            kmatrix[[j],[j+1]]=r[j+1]

            kmatrix[[j+1],[j]]=-r[j+1]

            #print kmatrix

        M = (2/9)*kmatrix

        #print M

        s=M.eigenvalues()

        #print s    

        lp3=6*10^-104

        for j in range(d):

            e= sqrt(s[j])

            vol = lp3*e

            volume = numerical_approx(vol, digits=2)

            if e.imag() ==0:

                print "volume eigenvalue =",(e)

                print "volume of tetrahedron =", volume