# A question from Hilbert and Courant's Vol II of Methods of Mathematical Physics (I might have spotted an error)

In page 751 (I hope some folks have a copy of it, legal or otherwise, I have a legal one :-D), I am attaching scans of pages 750-751.

Anyway, I don'tunderstand two things, the equation in page 751, the RHS of $u(x_0,0,0,t_0)$, in $\psi$, shouldn't the x-component be $\alpha t_0/2 + x_0$? and in the second term shouldn't it be just $\alpha t_0 \psi_x$?

Here is my reasoning, the x-component should be calculate according to Lorentz transformation in page 750:

$$x = \frac{t_0}{\sqrt{t_0^2-x_0^2}} (\frac{\alpha}{2}\sqrt{t_0^2-x_0^2})+\frac{x_0}{\sqrt{t_0^2-x_0^2}}\sqrt{t_0^2-x_0^2}=t_0 \alpha/2 +x_0$$

and as for the second term there, I might be wrong but:

$$\chi_{x'} = \psi_{x'} = \psi_x \frac{\partial x}{\partial x'} = \frac{t_0}{\sqrt{t_0^2-x_0^2}} \psi_x$$

So shouldn't it be $\alpha t_0 \psi_x$, instead of $(\alpha t_0+x_0) \psi_x$.

I guess I missed something.