Normalisation constant~ help

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Normalisation constant~ help~~

Homework Statement



An electron is in the spin state |> = A (3i, 4), so determine the normalisation constant A.

Homework Equations



:uhh: :frown:

The Attempt at a Solution



:cry: Well, I get confused about this questions, can anybody tell me what the normalisation constant is in this case? And does "in the spin state" mean something for given condition? Thanks a lot.
 

Answers and Replies

  • #2
Hootenanny
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Homework Statement



An electron is in the spin state |> = A (3i, 4), so determine the normalisation constant A.

Homework Equations



:uhh: :frown:

The Attempt at a Solution



:cry: Well, I get confused about this questions, can anybody tell me what the normalisation constant is in this case? And does "in the spin state" mean something for given condition? Thanks a lot.
Spin is simply a property that particles posses and this "spin state" describes, well the state of the spin of a particle or system of particles.

As for the question, what does one normally mean when one says a "normalisation constant". What does it mean in the context of a wave function for example?
 
  • #3
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Well, thanks a lot, but i dont think this problem is discussing about wave function, I cannot find any concept about wave function in my lecture notes. Thus, I consider that this question is only about math and calculation. Or maybe you can teach me some about the wave function or any other ideas? Thanks any way~
 
  • #4
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Do you know about complex vectors? And how to normalize those to unit length?
 
  • #5
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yes, o! you mean I can just do it like A = 1/|(3i, 4)|?? Thanks!
 
  • #6
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Yep, that's all there is to it. But don't forget to simplify that expression for A you got now.
 
  • #7
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Thanks, so it's A = 1/5
 
  • #8
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So in Physics we can write the spin state as a function of the particle:

[tex]|\psi \rangle = A \left ( \begin{array}{cc} 3i \\ 4 \end{array} \right)[/tex]

But wave function must integrate to unity over all space, so:

[tex]\langle \psi | \psi \rangle = 1 = A^2\left ( \begin{array}{cc} -3i & 4 \end{array} \right) \left ( \begin{array}{cc} 3i \\ 4 \end{array} \right) = 25A^2[/tex]

So I agree with your answer
 
  • #9


So in Physics we can write the spin state as a function of the particle:

[tex]|\psi \rangle = A \left ( \begin{array}{cc} 3i \\ 4 \end{array} \right)[/tex]

But wave function must integrate to unity over all space, so:

[tex]\langle \psi | \psi \rangle = 1 = A^2\left ( \begin{array}{cc} -3i & 4 \end{array} \right) \left ( \begin{array}{cc} 3i \\ 4 \end{array} \right) = 25A^2[/tex]

So I agree with your answer


I friggin get it now!
 

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