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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?

SuperCiocia
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Tomáš Kubalík
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    see https://physics.stackexchange.com/questions/364208/understanding-diracs-notation/364219#364219. Since $\psi(x,y,z,t)$ depends on 4 variable what is the sense of $\psi(x_1)$ depending on a single variable? – ZeroTheHero Apr 06 '20 at 04:51

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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 $\psi(\mathbf x) = \langle \mathbf x |\psi\rangle$.

Charles Francis
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  • Thanks for your answer. Is this notation correct? ψ(x,y,z,)↔ |x,y,z⟩ Or should I write three different signs for functions instead of x, y, and z. – Tomáš Kubalík Apr 06 '20 at 23:00
  • it is one function of three parameter, but it would be better to think of it as one function of a vector parameter. – Charles Francis Apr 07 '20 at 05:30