# Schrodinger equation normalization to find A -Griffiths

## Homework Statement

In David Griffiths Introduction to Quantum Mechanics (2nd ed.), page 32 he normalizes a time independent wave function to get the coefficient A. He dropped the sine part of the integration with no explanation. What is the justification.

## Homework Equations

The time independant wave function given is $\varphi$ = Asin(kx)
Griffiths gets :
$\int^{a}_{0}|A|^{2}sin^{2}(kx) dx = |A|^{2}\frac{a}{2} = 1$
But:
cos(2kx) = 1 - 2sin$^{2}(kx)$
and:
sin$^{2}(kx) = \frac{1}{2} - \frac{1}{2}cos(2kx)$
This means that the integral should really give:
$|A|^{2}(\frac{a}{2} - \frac{1}{4k}sin(2ka))$

## The Attempt at a Solution

What is the justification for dropping the sine term.

## Answers and Replies

BruceW
Homework Helper
Should this be in the homework section? Anyway, with the information given, there is no justification. But I am guessing there is more information given in the book. Does it say anything about what the value of the wave function is when x=a?

vela
Staff Emeritus
Science Advisor
Homework Helper
Education Advisor
The spatial frequency k takes on only certain values in order to satisfy the boundary conditions. For those values, you have that sin(2ka)=0.

Yes at x=a, x=0
Also not sure where this should go. It is a clarification of the textbook not a homework problem. At least this was my reasoning. I've been wrong before.

Gary

Thank you Vela.
I had fogotten that. That makes sense. It's too bad that Griffiths didn't point this out. Generally the text is great, especially for self study but he sloughs thing sometimes.