4 ms·

They most likely said "The wave function is differentiable and its derivative is continuous", which isn't obvious. If you think that it sounded strange you shou

They most likely said "The wave function is differentiable and its derivative is continuous", which isn't obvious. If you think that it sounded strange you should have asked during the lecture and they would have explained. Now instead you just assumed that you knew better and made a fool of yourself... Also this isn't advanced mathematics, this is something most who are interested learns in high-school and I can assure you that most physics professors are aware of this fact.

graycat 10y ago
> They most likely said No, they said what I wrote they said. It was at YouTube, from MIT, from a course in quantum mechanics. Uh, I do understand this stuff: E.g., given a positive integer n, the set of real numbers R, the usual topology for R^n, a set C a subset of R^n closed in that topology, there exists a function f: R^n --> R so that for x in R^n, f(x) is 0 for x in C, f(x) > 0 for x not in C, and f infinitely differentiable. E.g., for n = 1, the result applies for set C a Cantor set or a Cantor set of positive measure. For n > 2, the result applies for a sample path of Brownian motion or the Mandelbrot set. When I was a grad student, I discovered and proved this result. Later I published the result in JOTA.
- selimthegrim 10y ago
  A bigger problem is the difference between Hermitian and self adjoint, a lot of physics professors don't understand that. Or for example, this famous dialogue between Geoffrey Chew and Arthur Wightman from the 1960s bootstrap fad: Wightman asked Chew: why assume from the start that the S-matrix was analytic? Why not try to derive it from simpler principles? Chew replied that "everything in physics is smooth". Wightman asked about smooth functions that aren't analytic. Chew thought a moment and replied that there weren't any.
- selimthegrim 10y ago
  By the way, the reason they said that was no doubt to motivate the students to choose correct boundary conditions for some Sturm-Liouville problem (as the previous poster sort of alluded to)

graycat 10y ago

> They most likely said No, they said what I wrote they said. It was at YouTube, from MIT, from a course in quantum mechanics. Uh, I do understand this stuff: E.g., given a positive integer n, the set of real numbers R, the usual topology for R^n, a set C a subset of R^n closed in that topology, there exists a function f: R^n --> R so that for x in R^n, f(x) is 0 for x in C, f(x) > 0 for x not in C, and f infinitely differentiable. E.g., for n = 1, the result applies for set C a Cantor set or a Cantor set of positive measure. For n > 2, the result applies for a sample path of Brownian motion or the Mandelbrot set. When I was a grad student, I discovered and proved this result. Later I published the result in JOTA.

selimthegrim 10y ago
A bigger problem is the difference between Hermitian and self adjoint, a lot of physics professors don't understand that. Or for example, this famous dialogue between Geoffrey Chew and Arthur Wightman from the 1960s bootstrap fad: Wightman asked Chew: why assume from the start that the S-matrix was analytic? Why not try to derive it from simpler principles? Chew replied that "everything in physics is smooth". Wightman asked about smooth functions that aren't analytic. Chew thought a moment and replied that there weren't any.
selimthegrim 10y ago
By the way, the reason they said that was no doubt to motivate the students to choose correct boundary conditions for some Sturm-Liouville problem (as the previous poster sort of alluded to)