The Analytical Function Defined in the Hamilton-Jacobi and Schrödinger Approach and the Classical Schrödinger Equation - Bulnes, J.D.; Travassos, M.A.I.; Juraev, D.A.; López-Bonilla, J.L. (Karshi Multidisciplinary International Scientific Journal, 2024)
In this paper, we show that a specific extension of the Schrödinger ansatz fortwo free particles, under the requirement that this function (ansatz) be analytical, is compatible with the expected physical result for a quantum description at the quantum-classical boundary; that is, its total erasure in the transition to a description compatible with classical physics. Using the Cauchy-Riemann relation, the Laplace equation, and the Hamilton-Jacobi equation, we have shown that this function verifies a classical equation arising from the time-dependent Schrödinger equation, since in the assumed context the time variable can be taken as a parameter since it is irrelevant in the process of approximation to the quantum-classical boundary.