API Reference: Quantum Mechanics¶

The Python surface exposes quantum-mechanics routines at top level (from pysicrs import pauli_matrices). See also Algorithms: Quantum Mechanics.

import pysicrs

Pauli algebra & density matrices¶

pauli_matrices() -> (sx: list[list[complex]], sy, sz)

The three Pauli matrices as complex 2×2.

sx, sy, sz = pauli_matrices()
print(sx)   # [[0,1],[1,0]]

density_matrix(psi_real: list[float], psi_imag: list[float]) -> list[list[complex]]

Projective density matrix \(\rho = |\psi\rangle\langle\psi|\).

coherent_state(alpha_real: float, alpha_imag: float, n_terms: int)
    -> (real: list[float], imag: list[float])

Glauber coherent state \(\sum_n c_n |n\rangle\) in the Fock basis \(c_n = e^{-|\alpha|^2/2}\alpha^n/\sqrt{n!}\). Returns two equal-length lists.

re, im = coherent_state(1.0, 0.0, 20)
norm = sum(a*a + b*b for a, b in zip(re, im))
print(norm)           # ≈ 1.0

number_state(n: int, dim: int) -> (real: list[float], imag: list[float])

Fock state \(|n\rangle\) in dimension dim.

feynman_propagator_scalar(p_squared: float, mass: float, epsilon: float = 1e-9)
    -> complex

Scalar momentum-space Feynman propagator \(\frac{i}{p^2 - m^2 + i\varepsilon}\). Returns complex (Python complex, not a pair).

free_propagator_position(r: float, mass: float) -> float

Euclidean 4D position-space propagator \(\frac{m}{4\pi^2 r}K_1(mr)\) (massless limit fallback \(1/(4\pi^2 r^2)\) when \(mr\to 0\)).

function	purpose
`spin_operators`	\(S_a = \tfrac{\hbar}{2}\sigma_a\)
`partial_trace`, `purity`	entanglement diagnostics
`inner_product`, `projector`	Hilbert-space ops
`rayleigh_schrodinger_1st/2nd`	perturbation theory
`discretized_path_integral`, `effective_potential`, `wick_rotation`	path integrals
`free_propagator_momentum`, `photon_propagator_feynman`	field propagators