QM Sakurai 1.9 - Problem at last step only

  • Thread starter Thread starter alienskin562
  • Start date Start date
  • Tags Tags
    Qm Sakurai
Click For Summary

Homework Help Overview

The discussion revolves around a quantum mechanics problem from Sakurai, specifically focusing on the relationships between coefficients in an eigenvector equation. The original poster expresses difficulty in solving for the coefficients 'a' and 'b' and questions their non-algebraic relationship.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the redundancy of the eigenvector equations and the implications for expressing one coefficient in terms of the other. The normalization condition is also highlighted as a key constraint. Questions arise regarding the specific forms of 'a' and 'b' and how they relate to the expected solutions.

Discussion Status

Some participants have offered clarifications regarding the relationship between 'a' and 'b', suggesting that one can be expressed in terms of the other while adhering to the normalization condition. There is an ongoing exploration of how to arrive at the final form presented in Sakurai's work, with some participants questioning the specifics of the parameters involved.

Contextual Notes

Participants note the potential confusion stemming from the normalization condition and the specific forms of the coefficients as presented in the problem. The original poster's background in mathematics is mentioned, which may influence their approach to the problem.

alienskin562
Messages
4
Reaction score
0

Homework Statement



http://www.ocf.berkeley.edu/~yayhdapu/postings/sak19.gif

Homework Equations


The Attempt at a Solution


http://www.ocf.berkeley.edu/~yayhdapu/postings/sakurai1.9.pdf"
http://www.ocf.berkeley.edu/~yayhdapu/postings/sakurai1.9.docx"
These are here in this attached PDF. You can see where I'm stuck - how do I solve for a and b?? It just so happens that my BA is in math :(

http://www.ocf.berkeley.edu/~yayhdapu/postings/sak19_2.gif

a and b are related non-algebraically, no?
 
Last edited by a moderator:
Physics news on Phys.org
These two equations are actually redundant, as an eigenvector equation is supposed to be.

You can express 'b' in terms of 'a' or vice versa, and an additional constraint comes from the normalization condition |a|^2 + |b|^2 = 1.
 
Hey thanks, I'm such a n00b. Cleared up now.
 
How about clearing it up for me?
 
Its just this Bill - since the eigenvalue equaiton is redundant, you can go ahead and specify either a or b as long as the normalization condition is still satisfied.

So, since its a free parameter, you set a equal to the expected solution eigenket, a=cos beta

Then you solve for b.
 
If a = cos(β), then how do you get it into the final form given by Sakurai? Because his form has a = cos(β/2)
 
I just forgot the /2 :p
 

Similar threads

  • · Replies 10 ·
Replies
10
Views
4K
  • · Replies 3 ·
Replies
3
Views
3K
  • · Replies 7 ·
Replies
7
Views
5K
  • · Replies 10 ·
Replies
10
Views
11K
  • · Replies 3 ·
Replies
3
Views
2K
Replies
1
Views
2K
  • · Replies 16 ·
Replies
16
Views
2K
Replies
2
Views
3K
Replies
2
Views
4K
Replies
2
Views
2K