I must normalize this to solve for the normalization constant

[Void123]

Homework Statement

A hydrogen atom given the following state:

$$\psi (r, 0) = A\psi_{100}(r) + (\frac{1}{\sqrt{5}})\psi_{311}(r) + (\frac{1}{\sqrt{3}})\psi_{422}(r)$$

I must normalize this to solve for the normalization constant $$A$$

Homework Equations

The Attempt at a Solution

Is it just me or does the integral turn out to be as hellish as it seems? Am I supposed to integrate the whole expression or just the first term?

 

[Redbelly98]

You must integrate the whole expression, since the normalization condition is

∫ψ*·ψ = 1​

But this is not a hellish problem. Here are two easy questions, the answers to which are probably easier than you'd think:

1. What is the value of

∫ψ₁₀₀*·ψ ₁₀₀ = ____?​

2. What is the value of

∫ψ₁₀₀*·ψ₃₁₁ = ____?​