Is this expression about 3D quantum wave correct? $ \psi( x, y, z, t ) \leftrightarrow │\psi\rangle$

Question

I am pretty sure that a one-dimensional variant is correct $ \psi( x, y, z, t ) \leftrightarrow │\psi\rangle$. It looks like an infinite column of complex numbers. I would like to know if its also true for $ \psi( x, y, z, t ) \leftrightarrow │\psi\rangle$. First entry in my column vector would be $\psi(x_1)$ times $\psi(y_1) \times \psi(z_1)$. What would be the second entry?

Answer 1

The entries at time $t$ are $\psi(x,y,z,t)$. The arrangement of as a column vector, or as a three dimensional array, is essentially arbitrary. You may find it easier to think of it as a three dimensional array.

It is more usual to use vector notation $\mathbf x = (x,y,z) = (x^1,x^2,x^3)$, then the correspondence is $\psi(\mathbf x) = \langle \mathbf x |\psi\rangle$.