Before revision:  Results, obtained by solving explicitly the Schr\"odinger equations by means of spectral decomposition of the Hamilton operator, coincides with those obtained by solving the stochastic Euler Lagrange equations derived by a variational principle and providing therefore consistency . Arbitrage bubbles are computed .
After revision:  Results, obtained by solving explicitly the Schr\"odinger equations by means of spectral decomposition of the Hamilton operator, coincides with those obtained by solving the stochastic Euler Lagrange equations derived by a variational principle and providing therefore consistency .