formality of "one"

[57730]

Is there any difference in formality when considering the following sentences:
(1)-One can do great things if they just have enough patience.
(2)-You can do great things if you just have enough patience.
To clarify, I consider the second sentence when it is used to state a general fact, and not to adress a specific locutor.

Which version would be found in a science textbook, when the author would be stating a fact? For example:
-One can normalize the result to find the wave function.
-You can normalize the result to find the wave function.

 

[5jj]

(1)-One can do great things if they just have enough patience.

That is incorrect in BrE. The correct version is One can do great things if one just has enough patience

 

[5jj]

-One can normalize the result to find the wave function.
-You can normalize the result to find the wave function.

I think a scientist is more likely to write It is possible to normalize .... or The result can be normalized to ... .

[Not a scientist]

 

[probus]

I very much doubt that the version with you would occur in academic discourse, although it is far more common in everyday usage. I think many people consider this use of one stuffy and old-fashioned.