Why Can't the Probability Exceed 1 in Time-Dependent Perturbation Theory?

[ehrenfest]

[SOLVED] time-dependent perturbation theory

Homework Statement

My book uses time-dependent perturbation theory to derive the following expression for the transition of \psi_{100} to \psi_{210} in the hydrogen atom in a uniform magnetic field with magnitude $$\mathcal{E}$$

$$\frac{131072}{59049} \frac{e^2 \mathcal{E}^2 a_o^2}{(E_2 -E_1)^2} \sin^2(\frac{E_2-E_1}{2 \hbar}t)$$

What I don't understand is why you cannot just increase $$\mathcal{E}$$ until the probability goes above 1?

Homework Equations

The Attempt at a Solution

 

[Dick]

Because it's 'perturbation theory'. If the field becomes large, then whole approximation that the field can be treated as a 'perturbation' goes out the window and the formula is invalid.