'Particle in a box' probability problem?
I have learned how to determine the probability of finding a particle in an infinitely high box across a range i.e. from 0 to L/2. However I have been given a problem which asks me to determine the probability for a particle at exactly L/2.
I can't figure out how I can do this. Any suggestions?
- supastremphLv 61 decade agoFavorite Answer
You shouldn't be able to figure out how to do this, since the problem is ill posed without some interval of observation. The probability of finding it in an exact spot approaches zero.
- oldprofLv 71 decade ago
I vaguely remember your problem from one of my classes, but I don't recall the specifics. Anyway I can tell you the probability of locating a particle at a specific location is zero. I can't give you a math proof, but I can offer a thought experiment.
Suppose we have a circle of a uniform probability distribution with diameter D. As the probability of finding a particle, a point, anywhere within that circle is p(A) = A/A = 1.0000, the probability of finding that particle in a sub area a < A is p(a) = a/A = pi (d/2)^2//pi (D/2)^2 = (d/D)^2
As you can see, as a gets smaller and smaller, and we converge on a single dimensionaless point, d approaches zero. In which case p(point) = (0/D)^2 = 0
- ?Lv 44 years ago
oldprof is i think of fake effect the subject. regularly those form of questions are no longer with regard to the possibility of the particle being in a particular place, yet extremely interior a undeniable area. that's Non-0
- fizixxLv 71 decade ago
It's simple Wave Mechanics. One of the easiest problems in Quantum Mechanics.
Look it up on Google. There must be tons and tons of sites about this.
- How do you think about the answers? You can sign in to vote the answer.
- Anonymous1 decade ago
take the original answer and divide by two