Abstract
A quantum mechanical wave function is shown to approximate affine nonlinear optimal feedback, when an absolute value of the terminal wave function is set positive and with no singular dependence on a control constant HR. The wave function is explicitly written down according to a path integral method and a stationary phase approximation of the integral. It is shown that a phase of the wave function approximates in HR → 0 to a Hamilton-Jacobi value function. We can phase the quantum mechanical fluctuation out in the limit. It is simple to take the terminal absolute value function that meets the condition of having no singularity at HR=0. This is because the terminal absolute value function without any dependence on the constant HR apparently satisfies the no singularity condition. Although we restrict ourselves with a scalar system, generalization to a system with higher dimensionality is straightforward.
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