Time-of-flight spectroscopy using neutrons produced by a spallation source is used to measure the one-magnon scattering throughout the Brillouin zone for La2Cu04. The zone-boundary magnons have an energy ^WZB~0.3 12 ±0.005 eV and are good eigenstates of the quantum Heisenberg Hamiltonian in that they possess lifetimes > \Q/(o. A multiplicative renormalization of the overall frequency scale of classical spin-wave theory accounts for the quantum effects in the one-magnon spectrum.PACS numbers: 75.30.Ds, 74.70.Vy, 75.10.Jm, 75.50.Ee The unusual features of Heisenberg antiferromagnets when quantum mechanics is taken into account have been investigated for much of this century. For the onedimensional case, quantum fluctuations destabilize the Neel state entirely. Even in higher dimensions, quantum fluctuations lead to significant corrections to the groundstate energy [1,2] and the spin-w^ave excitations [3] which are strongest for low spin. The discovery of hightemperature superconductivity has focused attention on La2Cu04, apparently an excellent realization of a twodimensional (2D) spin-y quantum antiferromagnet [4]. The magnetic correlations in La2Cu04 have been investigated by several microscopic techniques, most notably light scattering [5], muon spin relaxation [6][7][8], and neutron scattering [9][10][11][12][13]. Unfortunately, because of experimental limitations and restrictions in momentum and energy transfer, no technique has been able to probe the excitations over the whole Brillouin zone. We describe here a neutron-scattering investigation performed on a spallation source, in which we were able to overcome previous difficulties and observe magnetic excitations over a wide range of wave vector and energy. Well-defined zoneboundary spin waves with an energy of /ift)zB=0.312 ±0.005 eV are found. Also, the dispersion relation shows the conventional spin-wave form.Following previous practice, we use the orthorhombic nomenclature to label reciprocal space so that the basal planes are parallel to the (AO/) zone. Even though a^c, in this experiment we do not distinguish between them, for convenience, we define a* and c* to lie in the horizontal and vertical planes of the instrument, respectively. The sample was an assembly of sixteen single crystals [14] aligned such that their in-plane axes coincided to better than 1.5°. The total mass of the crystals was 0.1 kg. As described elsewhere [12], crystals were grown from CuO-rich melts contained in a large Pt crucible. The room-temperature lattice parameters were a=5.375(2) A, * = 13.156(4) A, and c=5.409(2) A. The Neel temperatures of the individual crystals ranged between 260 and 290 K.Experiments were performed on the High-Energy Transfer Spectrometer (HET) [15] at the United Kingdom spallation neutron source ISIS of the Rutherford Appleton Laboratory. HET is a "direct geometry chopper" spectrometer. High-energy (spallation) neutrons are produced when an 800-MeV pulsed proton beam with a current of 100 juA hits a uranium target. A beam of monochromatic neutrons...