Question

Give me thee relation of the position particle in space according to the Erwin Schroedinger's or Give Erwin Schroedinger's equation of the position of the particle in space​

Answer 1

The most famous example is the nonrelativistic Schrödinger equation for the wave function in position space ${\displaystyle \Psi (\mathbf {r} ,t)}$ of a single particle subject to a potential ${\displaystyle V(\mathbf {r} ,t)}$, such as that due to an electric field.[6][note 2]

Time-dependent Schrödinger equation in position basis
(single nonrelativistic particle)

${\displaystyle i\hbar {\frac {\partial }[\tex] [tex]{\partial t}}$ $\Psi (\mathbf {r} ,t)=\left[{\frac {-\hbar ^{2}}{2m}}\nabla ^{2}+V(\mathbf {r} ,t)\right]\Psi (\mathbf {r} ,t)}$

where ${\displaystyle m}$ is the particle's mass, and ${\displaystyle \nabla ^{2}}$ is the Laplacian.

This is also a diffusion equation, but unlike the heat equation, this one is also a wave equation given the imaginary unit present in the transient term.

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