Normalization constant A of a harmonic oscillator

[Sorin2225]

Homework Statement

Finding the normalization constant A of a harmonic oscillator

Relevant Equations

(psi(x,t))^2=1

I've worked through it doing what I thought I should have done. I normalized the original wavefunction(x,0) and made it = one before using orthonormality to get to A^2(1-1) because i^2=-1 but my final answer comes out at 1/0 which is undefined and I don't see how that could be correct since A is meant to be a real number. I'm not really sure where I've gone wrong either so any insight would be appreciated.

 

[vela]

$\lvert \psi_1 + i \psi_4 \rvert^2 \ne (\psi_1 + i \psi_4)^2$

The vertical lines matter.

 

[Sorin2225]

So it's the absolute value? which means that it's +1 not -1?

 

[vela]

What is “it”?

 

[Sorin2225]

|iψ4*iψ4|

 

[vela]

That's not how absolute values work. You can't say $\lvert a+b \rvert = \lvert a \rvert + \lvert b \rvert$ in general.

How do you calculate the modulus of a complex number?

 

[Sorin2225]

sqrt(a^2+b^2) so it would be Sqrt((i^2)^2+((psi(4)^2)^2))

 

[kuruman]

$|\Psi|^2=\Psi^*\Psi=[A(\psi_1+i\psi_4)][A^*(\psi^*_1-i\psi^*_4)]$. What do you get when you multiply it out?