  We pursue the quantum-mechanical challenge to the efficient market hypothesis
for the stock market by employing the quantum Brownian motion model. We utilize
the quantum Caldeira-Leggett master equation as a possible phenomenological
model for the stock-market-prices fluctuations while introducing the external
harmonic field for the Brownian particle. Two quantum regimes are of particular
interest: the exact regime as well as the approximate regime of the pure
decoherence ("recoilless") limit of the Caldeira-Leggett equation. By
calculating the standard deviation and the kurtosis for the particle's position
observable, we can detect deviations of the quantum-mechanical behavior from
the classical counterpart, which bases the efficient market hypothesis. By
varying the damping factor, temperature as well as the oscillator's frequency,
we are able to provide interpretation of different economic scenarios and
possible situations that are not normally recognized by the efficient market
hypothesis. Hence we recognize the quantum Brownian oscillator as a possibly
useful model for the realistic behavior of stock prices.
