Interference between different energy eigenstates in a quantum system results in an oscillation with a frequency which is proportional to the difference in energy between the states. Such an oscillation is observable in polarized positronium when it is placed in a magnetic field. In order to measure the hyperfine splitting of positronium, we perform the precise measurement of this oscillation using a high quality superconducting magnet and fast photon-detectors. A result of $203.324 pm 0.039rm{~(stat.)} pm 0.015rm{(~sys.)}$~GHz is obtained which is consistent with both theoretical calculations and previous precise measurements.
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