Context: postulates of quantum mechanics, wavefunctions.
Background: Engineering graduate student (Calc3, DiffEq, PDE).
2006-10-22 15:24:46 · 4 answers · asked by Enrique C 3 in Science & Mathematics ➔ Mathematics
a function is quadratically integrable means
it satisfies
The integral from -infinity to infinity of abs(f(x))^2 is < than infinity...in other words there is a definite solution...easier just to look at the source at wikipedia.
2006-10-22 15:42:27 · answer #1 · answered by pokerden1 2 · 0⤊ 0⤋
'Quadratically integrable' (or also 'square integrable') simply means that a tensor function can be described in terms of linear, cartesian metrics. If this were not the case, then linear superposition of wavefunctions couldn't happen. Think of the space F of all wave functions as a vector space. If α, à are contained in F, then a*α + b*à can be in F iff * and + are linear operators.
Doug
2006-10-22 22:53:34 · answer #2 · answered by doug_donaghue 7 · 0⤊ 0⤋
'Quadratically' or 'square' integrable simply means that |f(x)|^2 has a finite integral over whichever region you are integrating over. For one variable functions, this is usually -infty to +infty. For functions of three variables, it is usually over all of three-space.
2006-10-23 08:31:37 · answer #3 · answered by mathematician 7 · 0⤊ 0⤋
It means the equation has a rational solution.
2006-10-22 22:53:12 · answer #4 · answered by warmspirited 3 · 0⤊ 0⤋