An important concept in the inverse scattering transform is the Lax representation. The quantum inverse scattering method starts by the quantization of the Lax representation and reproduces the results of the Bethe ansatz. In fact, it allows the Bethe ansatz to be written in a new form: the algebraic Bethe ansatz. This led to further progress in the understanding of quantum integrable systems, such as the quantum Heisenberg model, the quantum nonlinear Schrödinger equation (also known as the Lieb–Liniger model or the Tonks–Girardeau gas) and the Hubbard model.