How is it possible for Born's interpretation of the wave function to be published after Schrödinger published his equation? If I am right Born published his interpretation of the wave function after Schrodinger published his wave equation. However, according to my QM textbook, all the expected values of quantities (like energy and momentum) are derived from Born's interpretation, i.e. the wave function can only make any sense with the statistical interpretation. So, how and why did Schrödinger derive his equation for a function whose interpretation did not exist at that time?
(Kindly pardon me if the question is stupid, I am just a beginner!)
 A: What I guessed in the comments was true. Schrödinger mentioned in his $1926$ paper (see below) that "the real continuous partition of the charge is a sort of mean$\dots$".
So he got the right equation but he interpreted it wrongly. He believed that in reality electron has a continuous charge distribution. But he did mention that "no very definite experimental results can be brought forward in favour of his hypothesis".
The following is a relevant excerpt from Schrödinger's $1926$ paper "An Undulatory Theory of Mechanics of Atoms and Molecules" in The Physics Review (Vol. $28$, No. $6$, pp. $1067$):

But this amounts to making the following hypothesis as to the physical meaning of $\psi$ which of course reduces to our former hypothesis in the case of one electron only: the real continuous partition of the charge is a sort of mean of the continuous multitude of all possible configurations of the corresponding point-charge model, the mean being taken with the quantity $\psi\psi$ as a sort of weight-function in the configuration space.
No very definite experimental results can be brought forward at present in favor of this generalized hypothesis. But some very general theoretical results on the quantity $\psi\bar{\psi}$ persuade me that the hypothesis is right. For example, the value of the integral of $\psi\bar{\psi}$, taken over the whole coordinate space proves absolutely constant (as it should, if $\psi\bar{\psi}$ is a reasonable weight function) not only with a conservative but also with a non-conservative system. The treatment of the latter will be roughly sketched in the following section.

