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how solutions of Schrodinger's equation contribute towards electron density curve of hydrogen atom?

how solutions of Schrodinger's equation contribute towards electron density curve of hydrogen atom?

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2 Answers

SAGAR SINGH - IIT DELHI
879 Points
11 years ago

Dear anurag,

 


The solution of the Schrodinger equation for the hydrogen atom is a formidable mathematical problem, but is of such fundamental importance that it will be treated in outline here. The solution is managed by separating the variables so that the wavefunction is represented by the product:

The separation leads to three equations for the three spatial variables, and their solutions give rise to three quantum numbers associated with the hydrogen energy levels.

 

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General quantum system

For a general quantum system:[2]

i\hbar\frac{\partial}{\partial t} \Psi = \hat H \Psi

where

[edit] Single particle in a potential

For a single particle with potential energy V, the Schrödinger equation takes the form:[3]

i\hbar\frac{\partial}{\partial t} \Psi(\mathbf{r},\,t) = -\frac{\hbar^2}{2m}\nabla^2\Psi(\mathbf{r},\,t) + V(\mathbf{r})\Psi(\mathbf{r},\,t)

where

Srinivas Rao
11 Points
11 years ago

schrodinger equation is a differential equation written in terms of electron wave function. So, the equation is a store house of information  about the revolving electron. As squre of amplitude speaks about the intensity of a wave, square of si gives probability of finding the electron.

4(pi) r2 gives area of sphere, 4(pi) r2 dr gives a volume segment. 

4(pi) r2 dr (si) square gives radial probability distribution in a volume segment with out the consideration of any direction, that is nothing but electron cloud density,

 

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