We present a ($1+1$)-dimensional quantum model designed to describe nonsequential double ionization (NSDI) in homonuclear diatomic molecules exposed to strong linearly polarized laser fields. Extending the restricted-geometry framework previously developed for atomic systems by Eckhardt and Sacha, our approach captures key features of NSDI, including the characteristic knee structure in double ionization yields. Despite its simplifying assumptions, the model shows good agreement with experimental data and proves particularly suitable for systems with $\sigma$-type orbital symmetry. It offers a computationally efficient tool for exploring multielectron dynamics in molecular systems.

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• Atomic & molecular processes in external fields
• Classical mechanics
• Multiphoton or tunneling ionization & excitation
• Strong field ionization & excitation