- #1
SeM
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?
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?
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?