• Support PF! Buy your school textbooks, materials and every day products Here!

Schrodinger equation normalization to find A -Griffiths

  • Thread starter Gary Roach
  • Start date
  • #1
20
0

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 [itex]\varphi[/itex] = Asin(kx)
Griffiths gets :
[itex]\int^{a}_{0}|A|^{2}sin^{2}(kx) dx = |A|^{2}\frac{a}{2} = 1[/itex]
But:
cos(2kx) = 1 - 2sin[itex]^{2}(kx)[/itex]
and:
sin[itex]^{2}(kx) = \frac{1}{2} - \frac{1}{2}cos(2kx)[/itex]
This means that the integral should really give:
[itex]|A|^{2}(\frac{a}{2} - \frac{1}{4k}sin(2ka))[/itex]

The Attempt at a Solution


What is the justification for dropping the sine term.
 

Answers and Replies

  • #2
BruceW
Homework Helper
3,611
119
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?
 
  • #3
vela
Staff Emeritus
Science Advisor
Homework Helper
Education Advisor
14,580
1,200
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.
 
  • #4
20
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
 
  • #5
20
0
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.
 

Related Threads on Schrodinger equation normalization to find A -Griffiths

Replies
0
Views
3K
Replies
1
Views
1K
Replies
33
Views
5K
  • Last Post
Replies
5
Views
960
  • Last Post
Replies
10
Views
3K
  • Last Post
Replies
4
Views
11K
Replies
9
Views
792
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
1
Views
1K
Top