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A two-dimensional coordinate system whose axes are the **wavenumbers** \(k_{\text y}\) and \(k_{\text x}\). The *allowed* wavenumber states (dots), are states that a free electron can occupy in a 2d crystal (with dimensions \(L_{\text y}\) and \(L_{\text x}\)). These discrete states of electrons result from solving the Schrödinger equation for a *free electron gas* with *periodic* boundary conditions.

Each state (represented by the dot) occupies a **reciprocal area** \( \mathcal{A_1} \) (in 3D: reciprocal volume and in 1D: reciprocal length) given by the distances to the neighboring states, i.e. in y-direction: \(2\pi / L_{\text y}\) and in x-direction \( 2\pi / L_{\text x} \).