- #1
BeauGeste
- 49
- 0
Consider
[tex]\langle x'|\hat{p} \hat{x} | x \rangle[/tex].
Are these steps correct?
1. [tex]\hat{x}[/tex] operates on the x eigenstate to get
[tex]\langle x'|\hat{p} x | x \rangle[/tex].
2. x is a c-number so can be pulled out to get
[tex]x \langle x'|\hat{p} | x \rangle[/tex].
3. [tex]x \langle x'|\hat{p} | x \rangle = x \frac{\partial}{\partial x'}\delta (x'-x)[/tex]
The part I'm most wary on is 2 where I pulled x out. It seems like the p operator is acting on it so I shouln't be able to do that.
Alternatively, could I do the following:
1. have p operate on [tex]\hat{x}[/tex] first to get
[tex] \frac{\partial}{\partial x'}x' \delta (x'-x)[/tex]
2. Which becomes
[tex] \delta (x'-x) + x' \delta'(x'-x)[/tex]
Is one of these two routes incorrect?
[tex]\langle x'|\hat{p} \hat{x} | x \rangle[/tex].
Are these steps correct?
1. [tex]\hat{x}[/tex] operates on the x eigenstate to get
[tex]\langle x'|\hat{p} x | x \rangle[/tex].
2. x is a c-number so can be pulled out to get
[tex]x \langle x'|\hat{p} | x \rangle[/tex].
3. [tex]x \langle x'|\hat{p} | x \rangle = x \frac{\partial}{\partial x'}\delta (x'-x)[/tex]
The part I'm most wary on is 2 where I pulled x out. It seems like the p operator is acting on it so I shouln't be able to do that.
Alternatively, could I do the following:
1. have p operate on [tex]\hat{x}[/tex] first to get
[tex] \frac{\partial}{\partial x'}x' \delta (x'-x)[/tex]
2. Which becomes
[tex] \delta (x'-x) + x' \delta'(x'-x)[/tex]
Is one of these two routes incorrect?