# The relation between the probability of a particle to the left or right and the potential [closed]

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.

• 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/…. Dec 3 '20 at 12:36
• @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. Dec 3 '20 at 12:42
• I’m voting to close this question because it belongs on physics.stackexchange.com 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.