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In L. D. Landau and E. M. Lifshitz Quantum Mechanics it is said about oscillation theorem, is there any short and simple way to prove it, which would be understandable for the 2nd year student of math/physics department?
As one can see it states that in bounded (let it be one dimensional) space $\psi$ function of the ground energy state have zero "zeroes" and in $n$th excited state have exactly $n$ "zeroes". How one can prove it in short and easy way?
Note: this is not a hometasklike question. This is a try to deeper understand the general physics course.