## probability vs probability density

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

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

Karina Kong 2H
Posts: 98
Joined: Thu Jul 25, 2019 12:16 am

### probability vs probability density

Could someone explain the difference between probability vs probability density? Thanks!

Heba Mengesha 3D
Posts: 50
Joined: Sat Sep 07, 2019 12:19 am

### Re: probability vs probability density

Probability density is a "density" function. While probability is a specific value. The probability density function for a given value of X represents the density of probability.

christabellej 1F
Posts: 109
Joined: Sat Aug 17, 2019 12:17 am

### Re: probability vs probability density

The probability density, symbolized by psi squared, is the probability that something will be found in a space divided by region volume. For example, if psi squared is 0, then there is a probability of 0 that the electron will be found in that space in that region's volume. Probability has no unit but probability density has units of volume^-1.

DHavo_1E
Posts: 118
Joined: Sat Aug 17, 2019 12:17 am

### Re: probability vs probability density

Karina Kong 1L wrote:Could someone explain the difference between probability vs probability density? Thanks!

Hi,

How I see it is probability density telling whether or not it is likely to be in a specific region of a volume, and probability as how much likely. For example, at a point, the probability density could be 0.3pm^-3 (not as likely, as it is measured from a scale from 0 (not there) to 1 (certainly there). To find probability, you would multiply by the volume of the area (0.3 pm^-3) x (2pm^3) = 0.6 , 3 out of 5 chances of being there.
- similar example found in the textbook