  Hamiltonian approach in quantum theory provides a new thinking for option
pricing with stochastic interest rates. For barrier options, the option price
changing process is similar to the infinite high barrier scattering problem in
quantum mechanics; for double barrier options, the option price changing
process is analogous to a particle moving in a infinite square potential well.
Using Hamiltonian approach, the expressions of pricing kernels and option
prices under Vasicek stochastic interest rate model could be derived. Numerical
results of options price as functions of underlying prices are also shown.
