from sympy import *
init_printing()

from sympy.physics.quantum import *
from sympy.physics.quantum.pauli import *

from sympy_quantum_utils import *

eps, delta, theta, Hsym, t = symbols("epsilon, delta, theta, H, t")
Omega = symbols("Omega", positive=True)
n = 6

sx, sy, sz = SigmaX(), SigmaY(), SigmaZ()

H = eps/2 * sz + delta/2 * sx

Eq(Hsym, H)

U = exp(I * theta/2 * sy)

hamiltonian_transformation_auto(U, sx)

hamiltonian_transformation_auto(U, sz)

H1 = hamiltonian_transformation_auto(U, H)

H1

H4 = collect(H1, (sx, sz))

H4

c, o = split_coeff_operator(H4.args[1])

Eq(c, 0)

Eq(tan(theta), delta/eps)

eq = Eq(theta, atan(delta/eps))

eq

H5 = simplify(H4.subs(theta, atan(delta/eps)))

H5

powsimp(simplify(H5.subs(eps, sqrt(Omega ** 2-delta ** 2))), force=True)

U

eq

%reload_ext version_information

%version_information sympy