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A Schr\"odinger-picture description of the evolving quantum state of Hawkingradiation is given, based on an ADM decomposition using time slicings thatsmoothly cross the horizon. This treatment avoids requiring a role fortrans-planckian modes, which can be viewed as artifacts of Hawking's originalcalculation, and also supports arguments that radiation from black holes isproduced in a "quantum atmosphere" with thickness comparable to the horizonsize, rather than microscopically far from it. Particularly explicit formulasare given for the two-dimensional analog of the Schwarzschild geometry. Thisanalysis is expected to generalize to other black holes, and to cosmology. Theresulting quantum evolution also provides important background forinvestigating corrections to the Hawking process, as are necessary forrestoring unitary evolution of black hole decay.

Schr\"odinger evolution of the Hawking state