Struct WignerFunction 

pub struct WignerFunction {
    pub state_description: String,
    pub grid_values: Vec<(f64, f64, f64)>,
    pub hbar: f64,
}

The Wigner quasi-probability distribution for a quantum state.

The Wigner function W_ρ(q, p) is the Weyl transform of the density matrix ρ: W_ρ(q, p) = (1/πℏ) ∫ ⟨q+y|ρ|q-y⟩ e^{2ipy/ℏ} dy. It is a real-valued function (not necessarily non-negative) on phase space ℝ².

Fields

state_description: String

Description of the quantum state.

grid_values: Vec<(f64, f64, f64)>

Sample values W(q_i, p_i) at a grid of phase space points (q, p, W).

hbar: f64

Planck constant ℏ used in the definition.

Implementations

impl WignerFunction

pub fn new(state_description: impl Into<String>) -> Self

Construct an empty Wigner function for the named state.

pub fn with_hbar(self, hbar: f64) -> Self

Set the Planck constant ℏ.

pub fn is_normalized(&self) -> bool

The Wigner function integrates to 1 over all of phase space: ∫ W dq dp = 1.

pub fn lower_bound(&self) -> f64

The Wigner function satisfies the uncertainty bound: W_ρ ≥ -1/(πℏ).

pub fn approximate_purity(&self) -> f64

Compute the approximate purity Tr(ρ²) = (2πℏ) ∫ W² dq dp from grid data.

Trait Implementations

impl Clone for WignerFunction

fn clone(&self) -> WignerFunction

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for WignerFunction

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.