Module spin 

Structs

BlochSphereRenderer

Render Bloch sphere as wireframe with state vector.

SpinChain

Heisenberg spin chain with nearest-neighbor coupling.

SpinState

Spin-1/2 state: |psi> = up|+> + down|->.

Functions

bloch_angles

Get Bloch sphere angles (theta, phi) from a spin state. |psi> = cos(theta/2)|+> + e^{i*phi}*sin(theta/2)|->

from_bloch

Create spin state from Bloch sphere angles.

larmor_precession

Larmor precession: time evolution in a magnetic field. H = -gamma * B.sigma, evolve by exp(-iHt/hbar). For simplicity, gamma*hbar/2 = 1, so omega = |B|.

pauli_x

Pauli X gate: |+> <-> |->

pauli_y

Pauli Y gate: |+> -> i|-> , |-> -> -i|+>

pauli_z

Pauli Z gate: |+> -> |+>, |-> -> -|->

rotate_spin

Rotate spin state about an axis by an angle. Uses the SU(2) rotation: exp(-i * angle/2 * n.sigma)

spin_expectation

Expectation value of spin along an axis: <S.n> = (hbar/2)*<psi|sigma.n|psi>. Returns the value in units of hbar/2 (i.e., between -1 and 1).

stern_gerlach

Stern-Gerlach measurement along an axis. Returns (collapsed state, outcome +1 or -1).