  Quantum theory is used to model secondary financial markets. Contrary to
stochastic descriptions, the formalism emphasizes the importance of trading in
determining the value of a security. All possible realizations of investors
holding securities and cash is taken as the basis of the Hilbert space of
market states. The temporal evolution of an isolated market is unitary in this
space. Linear operators representing basic financial transactions such as cash
transfer and the buying or selling of securities are constructed and simple
model Hamiltonians that generate the temporal evolution due to cash flows and
the trading of securities are proposed. The Hamiltonian describing financial
transactions becomes local when the profit/loss from trading is small compared
to the turnover. This approximation may describe a highly liquid and efficient
stock market. The lognormal probability distribution for the price of a stock
with a variance that is proportional to the elapsed time is reproduced for an
equilibrium market. The asymptotic volatility of a stock in this case is
related to the long-term probability that it is traded.
