-- Verify solutions to the Dirac equation gamma0 = ((1,0,0,0),(0,1,0,0),(0,0,-1,0),(0,0,0,-1)) gamma1 = ((0,0,0,1),(0,0,1,0),(0,-1,0,0),(-1,0,0,0)) gamma2 = ((0,0,0,-i),(0,0,i,0),(0,i,0,0),(-i,0,0,0)) gamma3 = ((0,0,1,0),(0,0,0,-1),(-1,0,0,0),(0,1,0,0)) phi = px x + py y + pz z - E t E = sqrt(px^2 c^2 + py^2 c^2 + pz^2 c^2 + m^2 c^4) psi1 = exp(i phi / hbar) (E/c + m c, 0, pz, px + i py) psi2 = exp(i phi / hbar) (0, E/c + m c, px - i py, -pz) psi3 = exp(i phi / hbar) (pz, px + i py, E/c - m c, 0) psi4 = exp(i phi / hbar) (px - i py, -pz, 0, E/c - m c) psi5 = exp(-i phi / hbar) (E/c - m c, 0, pz, px + i py) psi6 = exp(-i phi / hbar) (0, E/c - m c, px - i py, -pz) psi7 = exp(-i phi / hbar) (pz, px + i py, E/c + m c, 0) psi8 = exp(-i phi / hbar) (px - i py, -pz, 0, E/c + m c) D(psi) = 1/c dot(gamma0,d(psi,t)) + dot(gamma1,d(psi,x)) + dot(gamma2,d(psi,y)) + dot(gamma3,d(psi,z)) "Verify solutions (1=ok)" i hbar D(psi1) == m c psi1 i hbar D(psi2) == m c psi2 i hbar D(psi3) == m c psi3 i hbar D(psi4) == m c psi4 i hbar D(psi5) == m c psi5 i hbar D(psi6) == m c psi6 i hbar D(psi7) == m c psi7 i hbar D(psi8) == m c psi8