# Does a position operator exist?

1. Sep 1, 2009

### chrisphd

Does a position operator exist?

2. Sep 1, 2009

### Pengwuino

Re: Eigenfunction

What do you mean exist? I don't want to just blurt out "yes" to such a seemingly obvious question...

3. Sep 1, 2009

### chrisphd

Re: Eigenfunction

Does a position operator acting on a wavefunction give a position eignenfunction?

4. Sep 1, 2009

### Pengwuino

Re: Eigenfunction

Yes, if the wavefunctions are eigenfunctions of the position operator ;)

5. Sep 1, 2009

### PhaseShifter

Re: Eigenfunction

For the correct wavefunction (Dirac delta function), yes. For other wavefunctions, no.

6. Sep 1, 2009

### chrisphd

Re: Eigenfunction

7. Sep 1, 2009

### Pengwuino

Re: Eigenfunction

No... why would it?

8. Sep 1, 2009

### chrisphd

Re: Eigenfunction

9. Sep 2, 2009

### PhaseShifter

Re: Eigenfunction

No, the momentum operator does not collapse the wavefunction.

You just get a new wavefunction $$F'=p_{1}0.8a+p_{2}0.6b$$. (And you'd still have to normalize that.)

10. Sep 2, 2009

### chrisphd

Re: Eigenfunction

Mathematically that is what you get when you apply the momentum operator to the wavefunction F. However, I was actually thinking about physically measuring the momentum of the wavefunction, in which the wavefunction then collapses into a or b. So my quesiton is then, when the position of a wavefunction is measured, will the wavefunction likewise collapse into a position eigenfunction just as it would if it was a momentum measurement.

11. Sep 2, 2009

### PhaseShifter

Re: Eigenfunction

In principle it would, but unless it's trapped in an infinitely deep and infinitesimally narrow potential well, that eigenfunction won't be a stationary state, and will immediately evolve into something else. A wavefunction corresponding to an exactly defined position you would also have infinite uncertainty in momentum.

Essentially it would require a potential resembling the limiting case of an infinite square well, where the length of the well approaches zero.

12. Sep 4, 2009

### xepma

Re: Eigenfunction