A Comparison of the Schrödinger and the Black-Scholes Hamiltonian

In last physic's friday blog post A Black-Scholes Schrödinger equation we introduced a Black Scholes Hamiltonian. And as announced we will compare the properties of this equation with the properties of the Schrödinger equation. To have some comparison I write both Hamiltonians:

Time independent Schrödinger Hamiltonian

Black-Scholes Hamiltonian

Viewed as a quantum mechanical system, the Black–Scholes equation has one degree of freedom, namely x, with volatility being the analog of the inverse of mass, the drift term a (velocity-dependent) potential, and with the price of the option C being the analog of the Schrodinger state function. The Black–Scholes Hamiltonian is non-Hermitian due to the drift term.
We can also formulate the Black-Scholes equation using Dirac's notation:

Next week we will introduce stochastic volatility into our Quantum-Finance framework ...