# Simple Quantum Mechanics Problem

1. Sep 5, 2007

### Nothing000

1. The solution to Schrodinger's wave equation for a particular situation is given by $$\psi(x) = \sqrt{\frac{2}{a_{0}}} \cdot e^{\frac{-x}{a_{0}}}$$. Determine the probability of finding the particle between the limits $$0 \leq x \leq a_{0}$$

2. Relevant equations
$$\int_{- \infty}^{\infty} {(\psi(x)})^2 dx} = 1$$

3. The attempt at a solution
$$\int_{0}^{a_{0}} {(\sqrt{\frac{2}{a_{0}}} \cdot e^{\frac{-x}{a_{0}}}})^2 dx}$$
After evaluating that integral I am coming up with 0.864665. So wouldn't that mean that there would be an 86% probability of finding the particle in between those limits? Well, the answer in the back of the book is 4*10^(-14)%

Last edited: Sep 5, 2007
2. Sep 5, 2007

### Avodyne

You are correct. I note that, to do this problem, we must *assume* that x must be positive; then the wave function is correctly normalized. A well-written problem would have stated this clearly. And the answer in the back of this book (are you *sure* you looked up the correct problem number??) is nonsense.

What book is this? I like to learn which books to avoid ...

3. Sep 5, 2007

### Nothing000

So you are saying that MY answer is correct?!

The Book is Semi-Conductor Device Physics by Neamen

4. Sep 5, 2007