Simple Quantum Mechanics Problem

[Nothing000]

1. The solution to Schrödinger'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. Homework 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)%

 

[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 ...

 

[Nothing000]

So you are saying that MY answer is correct?!

The Book is Semi-Conductor Device Physics by Neamen

 

[Avodyne]

Yes, your answer is correct.

I assume you mean "Semiconductor Physics and Devices". From a customer review at amazon: "Perhaps the worst textbook I have ever had the misfortune to rely upon in an upper division EE class. ... This text lacks clarity, conciseness, logical flow, and is completely unreliable. Specific examples include not just one or two but at least 60 problems with incorrect answers listed in the back of the text." From another review: "I've seen better explanations of quantum physics written in crayon on bathroom walls."

Show this problem and the book's answer to your prof. Suggest reading the amazon customer reviews.

 

[Nothing000]

Awesome Avodyne. Thanks buddy.