for a particle in a one dimensional box...?

Question

the ground state wavefunction is phi=(2/a)^(1/2) sin ((pi*x)/a)
what is the probability that the particle is :

A) in the right half of the box?
B) in the middle third of the box?

you two are wrong...quantum mechanically speaking...

this is a phy chem problem, it wouldnt let me post it anywhere but here though...quantum mechanically, probability density, hbar, W(n)=sqrt(2/a)sin((n*pi*x)/a)

Answer 1

Ok, the other answerers weren't much help. Since I don't like to answer homework problems for people, here are some hints to help you out. First of all, remember that the probability is given by the square of the wavefunction. (Actually its the complex conjugate times the orginal wavefunction, but since there aren't any imaginary numbers in your phi you can just square phi) What does the graph of the square of your given wavefunction look like? You should be able to answer part A just by looking at the symmetry in the graph of your wavefunction. Part B will actually require some math...unless you're more clever than I am. :D To get the probability, you'll have to integrate phi squared over the middle third of your box. (from x=a/3 to x=2a/3) Just remember to check your answer by asking yourself if your answer makes any sense when you're done. Probabilities should be less than one and greater than zero...assuming that your wavefunction is normalized. (it looks like it is)

Answer 2

A one dimensional box has no right half or middle third.

It's a single point in space.

Answer 3

A one dimensional box prohibits any movement in X

Answer 4

One dimension is the infinite, un-thinkable and un-countable.