What is the Normalisation Constant for an Electron in Spin State?

[ZoroP]

Normalisation constant~ help~~

Homework Statement

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

Homework Equations

The Attempt at a Solution

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.

 

[Hootenanny]

Homework Statement

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

Homework Equations

The Attempt at a Solution

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?

 

[ZoroP]

Well, thanks a lot, but i don't 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~

 

[borgwal]

Do you know about complex vectors? And how to normalize those to unit length?

 

[ZoroP]

yes, o! you mean I can just do it like A = 1/|(3i, 4)|?? Thanks!

 

[borgwal]

Yep, that's all there is to it. But don't forget to simplify that expression for A you got now.

 

[ZoroP]

Thanks, so it's A = 1/5

 

[BerryBoy]

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

$$|\psi \rangle = A \left ( \begin{array}{cc} 3i \\ 4 \end{array} \right)$$

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

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

So I agree with your answer

 

[Panic Attack]

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

$$|\psi \rangle = A \left ( \begin{array}{cc} 3i \\ 4 \end{array} \right)$$

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

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

So I agree with your answer

I friggin get it now!