- #1

- 58

- 0

< x | f > = f ( x )

?

shouldn't it be the result of the integral from minus infinity to infinty on xf(x)?

but then it can't even be a function of x...

- Thread starter maria clara
- Start date

- #1

- 58

- 0

< x | f > = f ( x )

?

shouldn't it be the result of the integral from minus infinity to infinty on xf(x)?

but then it can't even be a function of x...

- #2

George Jones

Staff Emeritus

Science Advisor

Gold Member

- 7,392

- 1,018

Here, x is an "eigenvalue" of the position operator. What you need to use in the integral is not the eigenvaule, but the state that is the "eigenfunction" that corresponds to this eigenvalue.

< x | f > = f ( x )

?

shouldn't it be the result of the integral from minus infinity to infinty on xf(x)?

but then it can't even be a function of x...

What states are eigenstates of the position operator?

- #3

- 58

- 0

but I'm still confused: the definition of the bra-ket is simply the inner product of the functions you put there:

< f | g > = integral from minus infinity to infinity on f*g (f*=the complex conjugate of f).

So the product < x' | f > should be written as follows:

< delta (x-x') | f >...

why do they write the eigenvalue in the bra, and not the function itself?

- #4

Dick

Science Advisor

Homework Helper

- 26,260

- 619

They write the eigenvalue in the bra because they are too lazy to write the eigenfunction. Really, it's just a notational abbreviation.

but I'm still confused: the definition of the bra-ket is simply the inner product of the functions you put there:

< f | g > = integral from minus infinity to infinity on f*g (f*=the complex conjugate of f).

So the product < x' | f > should be written as follows:

< delta (x-x') | f >...

why do they write the eigenvalue in the bra, and not the function itself?

- #5

- 58

- 0

everything makes much more sense now, thanks a lot!

- Last Post

- Replies
- 13

- Views
- 4K

- Last Post

- Replies
- 2

- Views
- 1K

- Last Post

- Replies
- 17

- Views
- 2K

- Last Post

- Replies
- 1

- Views
- 912

- Last Post

- Replies
- 3

- Views
- 1K

- Last Post

- Replies
- 0

- Views
- 1K

- Last Post

- Replies
- 1

- Views
- 772

- Last Post

- Replies
- 1

- Views
- 952

- Last Post

- Replies
- 8

- Views
- 1K

- Last Post

- Replies
- 7

- Views
- 1K