from sympy import *
init_printing()

from sympsi import *
from sympsi.pauli import *

theta, t = symbols("theta, t")
eps, Delta, Omega = symbols("epsilon, Delta, Omega", positive=True)
Hsym = symbols("H")

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

H = -eps/2 * sz - Delta/2 * sx

Eq(Hsym, H)

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

hamiltonian_transformation(U, sx)

hamiltonian_transformation(U, sz)

H1 = hamiltonian_transformation(U, H)

H1

H2 = collect(H1.expand(), (sx, sz))

H2

c, o = split_coeff_operator(H2.args[0])

Eq(c, 0)

Eq(tan(theta), Delta/eps)

H3 = simplify(H2.subs(theta, atan(Delta/eps)))

H3

H3.subs(Delta, sqrt(Omega ** 2 - eps ** 2))

hamiltonian_transformation(U, sx)

hamiltonian_transformation(U, sz)

%reload_ext version_information

%version_information sympy, sympsi