  We demonstrate a novel compact solid-state laser source for high-resolution
two-photon spectroscopy of the $1S-2S$ transition in atomic hydrogen. The
source emits up to 20 mW at 243 nm and consists of a 972 nm diode laser, a
tapered amplifier, and two doubling stages. The diode laser is actively
stabilized to a high-finesse cavity. We compare the new source to the stable
486 nm dye laser used in previous experiments and record 1S-2S spectra using
both systems. With the solid-state laser system we demonstrate a resolution of
the hydrogen spectrometer of 6 \times 10^{11} which is promising for a number
of high-precision measurements in hydrogen-like systems.
