On a ``Hamiltonian path-integral'' derivation of the Schrödinger equation

MlURA Takashi

Kai C. Yung, Jick H. Yee

This paper describes our first-principles derivation of the Hamiltonian for the calculation of the bound states for a particle with a spatially varying mass in an arbitrary potential well. Our approach is based on the Feynman path-integral technique and results in a Hermitian form of the Schr\"odinger equation that conserves current at the boundary. We deduced the correct operator ordering for the Hamiltonian and found a correctional term that can be viewed as an effective potential.

淳 井上

Ognjen Vukovic

The following paper tries to derive a Black-Scholes equation by using tools of quantum physics pertaining in that sense to Hamiltonian operator, path integrals, completeness equation, introducing ket and bra vectors. Schrodinger Hamiltonian is presented and compared to Black-Scholes-Schrodinger Hamiltonian. Similarity was demonstrated and it was proved that Schrodinger Hamiltonian was Hermitian while Black-Scholes Hamiltonian was anti-Hermitian. By using Schrodinger equation, price of option was implemented in the Schrodinger equation and by using Black-Scholes Hamiltonian. Black-Scholes equation was derived and a new and really powerful approach was demonstrated that could have immense application in the quantitative analysis and asset pricing.

Atsushi Inoue

László Árpád Gergely