Quantum Mechanics (pt. 2)
So I'm not actually taking a quantum mechanics course this semester, but I have been reviewing it heavily since a lot of it is invoked in this solid state physics course. The book I've been using is better than the one we used when I took quantum mechanics. In the author's discussion of the one-dimensional harmonic oscillator, he included the greatest footnote I've ever seen in a physics textbook:
(d2Ψ/dξ2) - ξ2Ψ = -(2E/ħω)Ψ
The reader might be astute enough to spot* that one specific solution to this equation is of the form ψ∝exp[(−ξ2/2)] (with a corresponding energy E = (ħω/2) ).
*It is, in fact, quite unlikely that any normal reader could possibly be astute enough to spot this. The reason why the author is astute enough to spot this is, of course, because he knows the answer already.
That footnote came right after the discussion too, which makes it even funnier.
(d2Ψ/dξ2) - ξ2Ψ = -(2E/ħω)Ψ
The reader might be astute enough to spot* that one specific solution to this equation is of the form ψ∝exp[(−ξ2/2)] (with a corresponding energy E = (ħω/2) ).
*It is, in fact, quite unlikely that any normal reader could possibly be astute enough to spot this. The reason why the author is astute enough to spot this is, of course, because he knows the answer already.
That footnote came right after the discussion too, which makes it even funnier.