How to Interpret Wave Equations in Bras and Kets?

[atomicpedals]

My texts aren't exactly clear on how to handle equations of this sort:

|ψ>=c(1|1>+2|2>-3|3>)

How is one to interpret this? All I'm sure of is that |ψ> is ψ(x) and that c is the normalization constant (which would be solved for in the usual way). Any tips or pointers towards resources for further study are greatly appreciated!

 

[vela]

It's a vector equation, like
$$\vec{x} = c(1\vec{v}_1+2\vec{v}_2-3\vec{v}_3)$$
$\psi(x)$ is actually the amplitude $\langle x \vert \psi \rangle$. Consider
$$\vert \psi \rangle = \int dx\,\lvert x \rangle\langle x \rvert \vert \psi \rangle = \int dx\,\vert x \rangle \langle x \vert \psi \rangle = \int dx\, \psi(x) \vert x \rangle$$to see what $\psi(x)$ means in a linear algebra sense.