#math #quantummechanics
How do mathematicians feel about Dirac's delta function? Got any pointers to gaining a more precise, "mathy" understanding of it?
I've been reading Shankar's book on quantum mechanics (really like it). Dirac's delta function is something that has always bothered me somewhat, since it's not really a function.
@aleksi
Perhaps normal functions are actually a fluke and functions are simply things that you integrate. I mean in reality, you never measure any function at any exact point, you always take some average of values (how large your sensor is, how long it takes to take the reading, etc.). So perhaps it's normal functions that don't exist, and then the Delta function doesn't seem so bad, no?
@rednekulo
In the context of quantum mechanics (and physical reality, which seems to obey quantum mechanics) that may be indeed correct.
But there are many contexts where functions *are* evaluated at exact points, for example when evaluated by (non-quantum) computers or by people.
To me the most reasonable (concise, useful) definition of a function is still a mapping that can be evaluated at any point. So calling things like Delta function "generalized functions" seems appropriate.
