Hi, I have heard (or imagined) that a wavefunction, where Psi is on the y-axis and the positions x is naturally on the x-axis, is really a one-dimensional system in Physics (not in mathematics), because the signal or the oscillation of the wavefunction is not really a dimension, and only the position x makes any physical sense in a cartesian system . Is this correct?(adsbygoogle = window.adsbygoogle || []).push({});

If so, how can a wavefunction Psi(x) generate a one-dimensional subspace as such :

\begin{equation}

\mathcal{Y} = [ \phi | \phi = \beta \psi , \beta \in \mathbb{C} ]

\end{equation}

where \phi is a function of Y of norm 1 and beta is an arbitrary constant, thus defining the probability density of \psi?

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# A One-dimensional systems

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