Wavefunction after position measurement

[MHD93]

Suppose I have a particle confined between 0 and d on the x axis, and it has some wavefunction, if I measured the particle to be between some small interval [a, b], would the wavefunction collapse into a rectangle-like function with equal prob. density on the interval and zero outside? or what?

Suppose, instead, that I measured the region [a, b] and did NOT find the particle there, it is reasonable that the wavefunction would be affected (i.e. it must become zero on [a, b]). Right or wrong? and if right how will it look like?

 

[bhobba]

What do you mean by measure the particle in some small interval? Do you mean you have some measuring device that if the particle is between a and b returns yes? Or do you mean you have a measuring device that will tell the actual position between a and b? If the former then yes if the latter it will collapse to a Dirac Delta function at the measured position.

If you measure it and under either scenario its not between a and b then it will collapse to a wave-function that is zero between the area you measured the position.

Under both scenarios it will quickly spread via the Schrodenger equation.

Thanks
Bill

 

[MHD93]

Do you mean you have some measuring device that if the particle is between a and b returns yes?

Yes, I am talking about this.

...it will collapse to a wave-function that is zero between the area you measured the position

and elsewhere? this is my question.

 

[bhobba]

and elsewhere? this is my question.

What it was before - but that will quickly collapse into the solutions of a particle in the box via the Schrödinger Equation.

Thanks
Bill