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We study the quantum mechanics of homogeneous black hole interiors in the RSTmodel of 2D gravity. The model, which contains a dilaton and metric, includesradiation back-reaction terms and is exactly solvable classically. The reducedphase space is four dimensional. The equations for one pair of variables can betrivially solved. The dynamics of the remaining degree of freedom, namely thedilaton, is more interesting and corresponds to that of a particle on the halfline in a linear potential with time dependent coupling. We construct theself-adjoint extension of the corresponding quantized Hamiltonian andnumerically solve the time dependent Schr$\ddot{\mbox{o}}$dinger equation forGaussian initial data. As expected the singularity is resolved and theexpectation value of the dilaton oscillates between a minimum and maximum,which both gradually decrease with time due to the time dependence in thepotential. In the classical black hole spacetime, the maximum value of thedilaton corresponds to the size of the horizon while the minimum is thesingularity. The quantum dynamics, therefore, corresponds at the semi-classicallevel to an evaporating black hole. The rate of quantum fluctuations increasesas the system evolves but intriguingly, at longer times the expectation valueof the radius undergoes "revivals" in which the amplitude of oscillationsbetween minimum and maximum temporarily increases. These revivals are alsocharacteristic of the quantum dynamics of the {\it time independent} quantumlinear potential.

Quantum Mechanics of the Interior of the Russo-Susskind-Thorlacius Black Hole