What is probability density?

$H_{\psi }=E_{\psi }$

1-D: $E_{TOTAL}\psi (x)=E_{k}\psi (x)+V(x)\psi(x)=-\frac{h^{2}}{8\pi ^{2}m}\frac{d^{2}\psi(x)}{dx^{2}}+V(x)\psi(x)$

Louise Zhuang
Posts: 31
Joined: Fri Sep 28, 2018 12:28 am

What is probability density?

Why is the square of the wavefunction(psi) the probability density? What is it exactly? (I read the textbook but it doesn't make a lot of sense to me...)

Laura Gong 3H
Posts: 89
Joined: Fri Sep 28, 2018 12:26 am
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Re: What is probability density?

The probability density is a measure of the likelihood (probability) that a particle will be found at a particular location in space. In this case, where you would likely find an electron in the electron cloud.

deepto_mizan1H
Posts: 65
Joined: Fri Sep 28, 2018 12:16 am

Re: What is probability density?

There is a slight difference between psi and psi^2, which helps to understand Schrodinger's Equation conceptually. Psi itself is a wavefunction, which varies with position. Once we square this value it becomes only positive, and provides a dimensional model of the area we can probabilistically find an electron. Therefore psi^2 is probability density for a particle, most often an electron.