Interactive single-qubit visualiser: tune a Hamiltonian, pick $|\psi(0)\rangle$, and watch Schrödinger evolution on the Bloch sphere.
Open Qubit Evolution
The Hamiltonian, $H$ is the energy operator. For a single qubit it is a $2\times 2$ Hermitian matrix, a real linear combination of the identity and the Pauli matrices:
$$
I = \begin{bmatrix} 1 & 0 \cr 0 & 1 \end{bmatrix},\quad
\sigma_x = \begin{bmatrix} 0 & 1 \cr 1 & 0 \end{bmatrix},\quad
\sigma_y = \begin{bmatrix} 0 & -i \cr i & 0 \end{bmatrix},\quad
\sigma_z = \begin{bmatrix} 1 & 0 \cr 0 & -1 \end{bmatrix}.
$$
Users can fine-tune $\omega$, $\Omega_x$, $\Omega_y$, and $\varepsilon$ to form the Hamiltonian:
$$
H = \frac{\omega}{2}\sigma_z + \frac{\Omega_x}{2}\sigma_x + \frac{\Omega_y}{2}\sigma_y + \varepsilon I
$$
The sign of each Pauli coefficient sets the sense of rotation about that axis. The identity coefficient $\varepsilon$ is a global energy: it shifts $E_\pm = \varepsilon \pm \omega_R/2$ but does not rotate the Bloch vector. On the Bloch sphere the state precesses about $\vec{\Omega}$ at
$$
\omega_R = \sqrt{\omega^2 + \Omega_x^2 + \Omega_y^2},\qquad T = 2\pi/\omega_R.
$$