We report an analytical theory of linear emission of exchange spin waves from a Bloch domain wall, excited by a uniform microwave magnetic field. The problem is reduced to a one-dimensional Schrödinger-like equation with a Pöschl-Teller potential and a driving term of the same profile. The emission of plane spin waves is observed at excitation frequencies above a threshold value, as a result of a linear process. The height-to-width aspect ratio of the Pöschl-Teller profile for a domain wall is found to correspond to a local maximum of the emission efficiency. Furthermore, for a tailored Pöschl-Teller potential with a variable aspect ratio, particular values of the latter can lead to enhanced or even completely suppressed emission.Wave generation is both an essential topic in wave physics and a prerequisite of any technology exploiting waves. Conventionally, waves are excited using an antenna, with their wavelength being limited by the antenna's size. Alternatively, we could use an inhomogeneity (either deliberately introduced, or naturally-occuring) in the medium and then apply a uniform, oscillatory external field to generate a wave. Small wavelength excitations require equally small antennas or inhomogeneities to generate them.In magnonics [1][2][3], the study of spin waves, we are fortunate that inhomogeneities with nanoscale dimensions naturally occur in magnetic materials: domain walls. These inhomogeneities are the transition regions between domains of uniformly aligned magnetization, and can have dimensions down to a few nanometers, depending on the material. Domain walls have been studied in great detail, due to a number of interesting properties: their magnetic field and current-driven motion [4,5], their ability to channel spin waves [6][7][8], and the unusual reflectionless behavior for spin waves passing through them [9]. Recently, there have also been numerical [10,11] and experimental [12,13] reports of pinned domain walls generating spin waves, with wavelengths down to tens of nanometers [14]. The origin of the observed spin wave emission has typically been attributed to the domain wall oscillations, generated by the applied microwave magnetic field [10][11][12][13] or spin-polarized current [14,15].In this letter, we report an analytical theory that demonstrates emission of exchange spin waves from a Bloch domain wall driven by a uniform microwave magnetic field, as a result of a linear process. The problem is reduced to that of the Pöschl-Teller potential in a Schrödinger-like equation -an exactly solvable model, of particular interest in quantum mechanics [16] and optics [17,18]. This potential is mostly known for its peculiar property of 100% transmission of incident waves at any frequency, for certain parameters of the potential [19]. While forming such a potential in other systems is difficult, serendipitously the reflectionless Pöschl-Teller potential exactly describes the graded magnonic index profile [20] due to a Bloch domain wall, allowing the peculiar behavior to be both investigated a...