- #1
Stephen Wright
- 2
- 0
<Mentor's note: moved from a technical forum, therefore no template.>
I'm long out of college and trying to teach myself QM out of Shankar's.
I'm trying to understand the reasoning here because I think that I am missing something...
1.1.3
1) Do functions that vanish at the endpoints x=0 and L=0 form a vector space?
2) How about periodic functions? obeying f(0)=f(L) ?
3) How about functions that obey f(0)=4 ?
If the functions do not qualify, list what go wrong.
The first 2 questions seem straight forward. X and L go to zero, and outside those boundaries you would get the null vector. If the function is periodic, you are certain to return a vector in the f(x).
#3 is tripping me up. I thought of an example function... let's say f(x)=x+4, so f(0)=4.
How is this not a vector space?
I was told that if g(x) and h(x) were in the set of f(x), g(0)+h(0)=8 which is not 4.
I do understand how this proves anything? What am I misunderstanding?
I'm long out of college and trying to teach myself QM out of Shankar's.
I'm trying to understand the reasoning here because I think that I am missing something...
1.1.3
1) Do functions that vanish at the endpoints x=0 and L=0 form a vector space?
2) How about periodic functions? obeying f(0)=f(L) ?
3) How about functions that obey f(0)=4 ?
If the functions do not qualify, list what go wrong.
The first 2 questions seem straight forward. X and L go to zero, and outside those boundaries you would get the null vector. If the function is periodic, you are certain to return a vector in the f(x).
#3 is tripping me up. I thought of an example function... let's say f(x)=x+4, so f(0)=4.
How is this not a vector space?
I was told that if g(x) and h(x) were in the set of f(x), g(0)+h(0)=8 which is not 4.
I do understand how this proves anything? What am I misunderstanding?