Probability of finding particle

1. Oct 28, 2012

Aziza

This is example from my book:

For some particle, let ψ(x,0) = $\frac{1}{\sqrt{a}}$exp^(-|x|/a).

Finding the probability that the particle is found between -x0 and x0 yields a probability of 86.5%, independent of x0! But how can this be, since as x0 tends to infinity, the probability of finding the particle between negative infinity and infinity must be 1....so the probability suddenly jumps from 86% to 100%?

I am thinking that maybe this is not a valid wavefunction since it has a sharp point at x=0 and my professor said that the wavefunction cannot have any sharp bends...?

2. Oct 28, 2012

Staff Emeritus
It's not independent of x0. What is the role of a here?

3. Oct 28, 2012

Aziza

It is just a constant, sorry I forgot to mention that.

4. Oct 28, 2012

Aziza

5. Oct 28, 2012

Staff Emeritus
It's not just a constant. It plays a very important role. What is it?

Hint: what are its dimensions?

Note also that your original problem doesn't specify that x0 is a special value of x.

6. Oct 28, 2012

Aziza

ohhh i think i see...a is related to the max height of the curve which is itself related to x0 so as x0 increases the max height decreases, thus keeping the probability constant in that interval...right?

7. Oct 29, 2012

Bill_K

What you're calling 'a' is called x0 in the book. 'a' and x0 are exactly the same thing.