Infinite Square Well with an Oscillating Wall (Klein-Gordon Equation)

[Foracle]

TL;DR Summary

Numerical solution of the wavefunction blows up when the frequency of oscillation of the wall is high. What does this mean?

I am trying to numerically solve (with Mathematica) a relativistic version of infinite square well with an oscillating wall using Klein-Gordon equation. Firstly, I transform my spatial coordinate ## x \to y = \frac{x}{L[t]} ## to make the wall look static (this transformation is used a lot in solving non-static boundary condition in the non-relativistic case), which brings Klein-Gordon equation to :
Input :

Output :

All constants have been set to 1

I tried to solve this system where ##L(t)=2+sin(1000 t)## using NDSolve :

Then I plot my result as a function of ##(y,t)## :

The wavefunction ##\psi## blows up. This doesn't happen when I tune the frequency down to 1, ##L(t)=2+sin(t)##

My question is why does ##\psi## blow up when the frequency of the oscillation is high and what does it mean? Does it have anything to do with particle production? Or did I just mess up my code?

 

[Foracle]

I have located my error. It was the fact that when I set ##\omega## to 1000, the velocity of the wall, ##\dot{L} = \omega cos(\omega t) \ge 1##, which is not allowed in the units that I am working with ##(c=1)##.
The solution to this is just to set ##L(t) = \frac{1}{\omega} (2+sin(\omega t))##, and this disastrous result doesn't happen anymore.