- #1

- 3

- 0

- Thread starter alisa
- Start date

- #1

- 3

- 0

- #2

Tom Mattson

Staff Emeritus

Science Advisor

Gold Member

- 5,500

- 8

What do you mean " if x=x". x=xgiven that [x,p]=ih, show that if x=x,

- #3

- 13,023

- 576

It's the coordinate representation in which the Hilbert space is [itex] L^{2}(\mathbb{R},dx) [/itex]. The "x" operator is realized by a multiplication by "x". She's asked to prove that the most general representation of the momentum operator in this Hilbert space is the one written there.What do you mean " if x=x". x=xby definition.

- #4

Tom Mattson

Staff Emeritus

Science Advisor

Gold Member

- 5,500

- 8

OK, so then it should read something like "If [itex]\hat{x}|\psi>=x|\psi>[/itex]...", right?

Last edited:

- #5

- 13,023

- 576

Exactly. That's the spectral equation, but nonetheless, yes.

- Last Post

- Replies
- 7

- Views
- 824

- Last Post

- Replies
- 19

- Views
- 2K

- Last Post

- Replies
- 6

- Views
- 4K

- Last Post

- Replies
- 1

- Views
- 890

- Last Post

- Replies
- 3

- Views
- 936

- Last Post

- Replies
- 1

- Views
- 807

- Last Post

- Replies
- 1

- Views
- 1K

- Last Post

- Replies
- 1

- Views
- 875

- Last Post

- Replies
- 1

- Views
- 302

- Last Post

- Replies
- 20

- Views
- 3K