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We present a theory of collective spin excitations indiluted-magnetic-semiconductor quantum wells in which local magnetic momentsare coupled via a quasi-two-dimensional gas of electrons or holes. In the caseof a ferromagnetic state with partly spin-polarized electrons, we find that theGoldstone collective mode has anomalous $k^4$ dispersion and that for symmetricquantum wells odd parity modes do not disperse at all. We discuss the gap inthe collective excitation spectrum which appears when spin-orbit interactionsare included.Comment: 14 pages, 7 figures. Submitted to Phys. Rev. B, final versio

Theory of spin waves in diluted-magnetic-semiconductor quantum wells