The Conversion between Schrödinger Equation and F=ma

Abstract

The compatibility between quantum mechanics and classical mechanics is always worth discussing. Schrödinger equation (SE) can be derived from F=ma and T+V=E. Important classical physics formulas can be derived from the SE. The SE intuitively contains the mass m and the potential energy formula (this quality m can be large enough to enter the macro range and the potential energy comes from classical attraction). These three points determine that the SE is an organic combination of wave functions and classical mechanical laws. Based on this, it can be predicted that the SE, which can be used to describe macroscopic objects, can be established. It can be observed from the experiment of electron diffraction in a magnetic field that the volatility and property of moving electrons can be presented simultaneously. This experimental phenomenon, together with the mathematical analysis mentioned above, supports the conclusion that Newton's second law still applies in the microscopic world. According to the SE, it can be proven that "the energy of a moving particle described by the law of waves is equivalent to a multiple of its kinetic energy"; There is no absolute boundary between macro and micro (or classical and quantum), and they can be compatible.