Normalising and Probabilities of wavefunctions

[Sekonda]

Hey

My question is displayed below

I think I have done this right but I wanted to check, we have to normalise the wavefunction first and I think this is done by assuming each state is equally likely and so assigning some constant 'c' to premultiply each of the 3 states.

We need multiply each state by it's Bra form such that we get 3c^{2}=1 and so c=1/√3
and provided this is correct then the probability of attaining an eigenvalue ω=1 is just

√(2/3)

Is this correct? If not what am I doing/assuming which is wrong?

Thanks,
SK

 

[CFede]

It's correct. You are not assuming that every state is equally likely, you know it from the fact that all are multiplied by the same constant (in this case 1) in the non normalized wave function.

 

[Sekonda]

Cheers man, was thinking as I wrote that - that is was wrong... considering the question.

Thanks!
SK

 

[Oxvillian]

Don't forget to square to get the probabilities

 

[Sekonda]

Ahh yes of course!, I did it wrong initally anyway - should of written 2/3 - giving (2/3)^(2) =4/9 as the probability, 44.4%

I believe this is correct...

Cheers!
Sk

 

[Sekonda]

Or is this probability just 2/3? Can someone check this

Cheers!
SK

 

[CFede]

The probability is 2/3. There is no need to square anything if your performed the braket.

 

[Sekonda]

Cheers, thanks for that! Good to know i am now doing it the right way.

SK