Here we present inelastic neutron scattering measurements from thefrustrated, quantum spin-1/2 chain material linarite, PbCuSO_4(OH)_2. Time offlight data, taken at 0.5K and zero applied magnetic field reveals low-energydispersive spin wave excitations below 1.5meV both parallel and perpendicularto the Cu-chain direction. From this we confirm that the interchain couplingswithin linarite are around 10% of the nearest neighbour intrachaininteractions. We analyse the data within both linear spin-wave theory anddensity matrix renormalisation group theories and establish the main magneticexchange interactions and the simplest realistic Hamiltonian for this material.
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