  Using the one dimensional free particle symmetries, the quantum finance
symmetries are obtained. Namely, it is shown that Black-Scholes equation is
invariant under Schr\"odinger group. In order to do this, the one dimensional
free non-relativistic particle and its symmetries are revisited. To get the
Black-Scholes equation symmetries, the particle mass is identified as the
inverse of square of the volatility. Furthermore, using financial variables, a
Schr\"odinger algebra representation is constructed.
