For example, if the potential is a harmonic potential $V(x)=kx^2$.

How to calculate the probability to the left or right when the particle stays at the position $x_0$?. Here $x_0$ is a constant.

  • $\begingroup$ The probability is zero. A think you mean probability density. For the well known harmonic oscillator you can e.g. look it up at: en.wikipedia.org/wiki/…. $\endgroup$ Dec 3 '20 at 12:36
  • $\begingroup$ @Daniel Huber What I mean is not in the sense of mean probability. I want to simulate a particle in a harmonic potential. But I do not know how to calculate the probability to the left or right. $\endgroup$
    – Blueka
    Dec 3 '20 at 12:42
  • 4
    $\begingroup$ I’m voting to close this question because it belongs on physics.stackexchange.com $\endgroup$
    – N.J.Evans
    Dec 3 '20 at 13:44

The probability density is given by $\lvert \psi\rvert^2$, where $\psi$ denotes the wave function. Thus to find the probability to the right or left of a point $x_0$ you need to integrate $\int_{x_0}^{\pm \infty} \lvert \psi\rvert^2$. The link @Daniel Huber provided explains how to find the wave function from the potential, i.e. solving Schrodinger's equation.


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