# How to sum equal terms in a superposition state?

Suppose after some computation we get a superposition like $$\frac{1}{\sqrt{4}}(\left|00\right>+\left|00\right>+\left|10\right>+\left|11\right>)$$. How do we merge the same term in this superposition. Simply adding two coefficients does not work here as the superposition should equal to $$\frac{1}{\sqrt{2}}\left|00\right>+\frac{1}{\sqrt{4}}\left|10\right>+\frac{1}{\sqrt{4}}\left|11\right>$$. For the general case, is there a formula to merge two same term in a superposition?

Note that $$\dfrac{|00\rangle + |00\rangle + |10\rangle + |11\rangle}{\sqrt{4}} = \dfrac{2|00\rangle+ |10\rangle + |11\rangle }{2} = \begin{pmatrix}1 \\ 0 \\ 1/2 \\ 1/2 \end{pmatrix}$$ is not a quantum state as it is not normalized.
$$\frac{1}{\sqrt{4}}\left(\frac{\sqrt{2}}{2}|00\rangle+\frac{\sqrt{2}}{2}|00\rangle+|10\rangle + |11\rangle\right)$$.
\begin{align} H\frac{1}{\sqrt{2}}\left(|0\rangle+|1\rangle\right) &= \frac{1}{\sqrt{2}}\left(\frac{1}{\sqrt{2}}|0\rangle+\frac{1}{\sqrt{2}}|1\rangle+\frac{1}{\sqrt{2}}|0\rangle-\frac{1}{\sqrt{2}}|1\rangle\right) \\ &= \frac{1}{\sqrt{2}}\left(\frac{2}{\sqrt{2}}|0\rangle+\frac{0}{\sqrt{2}}|1\rangle\right) \\ &=\frac{2}{\sqrt{4}}|0\rangle = |0\rangle \end{align} where going from the first line to the second line was obtained by just adding the coefficients