## Schrodingers Equation and Probability Density

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

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

Kate_Santoso_4F
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### Schrodingers Equation and Probability Density

Based on the textbook, psi squared is the probability density, which means that wherever psi squared is large, the particle has a high probability density and wherever psi squared is small, the particle has a low probability density. What do these statements mean qualitatively in relation to the wave function of a particle?

Chem_Mod
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### Re: Schrodingers Equation and Probability Density

The wave function describes a physical wave in space along which the particle is spread out. We can use a wave function (Ψ aka height of the wave) in the Schrodinger equation to determine the probability of finding an electron in a specific location in an atom (ex. for a p-orbital, at x=0, since there's a node there, the Ψ^2=0, since height at x=0 is 0, Ψ=0).

505095972
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### Re: Schrodingers Equation and Probability Density

To add on to that, it basically helps calculate the orbital that a specific electron is in by telling us where the electron will probably be.