Can the Sigma Be Removed from the Normalization Equation for a Wavefunction?

[zahra95]

Homework Statement

the wavefunction

where <

|

> =

. I want to normalize it and find constant normalization A. A is real number.

Homework Equations

The Attempt at a Solution

I know that for normalizing the wave function

but what happen for sigma? can I remove it from equation?

 

[PeroK]

You can't just ignore the sigma! First, can you find an expression for $||\phi||^2$?

 

[zahra95]

I think the equation is :

because <

|

> =

is it correct? I'm not sure!
but what I do after that?

 

[PeroK]

I think the equation is :View attachment 95040because <

|

> =

is it correct? I'm not sure!
but what I do after that?

That's obviously not right. If you're stuck with an infinite sum, try a simple sum and see what happens. Try:
$\phi = A(\phi_0 + \frac{\phi_1}{3^4})$

 

[zahra95]

and

for n = 0,1
= A^2(1+1/3^8 + 1/5^8 + 1/7^8 + ... )
then it is true that = A^2(1/(2n+1)^8) isn't it?

 

[PeroK]

Was that integral sign in post #3 a typo?

For the next bit, trying googling "sums of reciprocal powers".