Probability of finding a particle [concept behind it]

[catsarebad]

okay so I'm having a bit hard time understanding this:

i get that probability of finding a particle in between [a,b] is integral (over a,b) (Ψ(x,t)*)Ψ(x,t) dx.

however, can it also be integral (over a,b) of (Ψ(x,0)*)Ψ(x,0) dx?

if not, why?

i saw an example where Ψ(x,0) was given and problem asked user to find prob between some interval. i noticed that the example found Ψ(x,t) first (using usual unitary operator e^(-ikE/h)). i don't understand why it can't be found right away from Ψ(x,0).

thanks a bunch!

 

[bhobba]

They are both correct. The second one is simply the first at time t=0.

Thanks
Bill

 

[catsarebad]

oh i see. mathematically, i suppose e^(-i) part always goes away so they have to be equal.

in terms of physics, could you give a quick reasoning for why this is true? why is the probability of finding a particle in interval [a,b] the same as the probability of finding the particle at time t=0 in same interval [a,b]? kinds having a hard time putting intuition behind it.
thanks.

 

[bhobba]

why is the probability of finding a particle in interval [a,b] the same as the probability of finding the particle at time t=0 in same interval [a,b]? kinds having a hard time putting intuition behind it.

It isn't.

Why would you think such a thing?

Thanks
Bill