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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.
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.
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