Graphs of Schrodinger's wave equation.

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Avatar of PrajjawalTiwari1

In the graphs of shi(r) vs r and shi²(r) vs r, the does the magnitude of local maxima increases or decreases with increase in r?

And is the result same in case of both shi(r) vs r and shi²(r) vs r?

And what is the reason behind it?

Note: please use simple words so that I can understand easily. It's not like i don't understand difficult words or that my vocab is weak, it's just that I prefer simpler words for understanding.

Thank you in advance🙏🙏🙏

Avatar of RoopTeraMastana2

They both decrease, and here's why:

Let's consider the shi(r) equation first. The function contains the coefficient of e^(-r/(na0)). Because of the negative sign on r as well as the fact that it is in the numerator in the exponent, the amplitude will decrease as you increase the radius.

The shi^2(r) function would produce this same effect, but the "damping" occurs even faster than in the first shi(r) function we looked at.

Hope this helps!