= Solution
A sudden wall displacement leaves the initial <wavefunction> unchanged: it is $\sqrt{2/L}\sin(\pi x/L)$ on $[0,L]$ and zero on $(L,2L]$. It is not an <eigenfunction> of the new <Hamiltonian>, so there is \b[no single certain new <energy>]. Its <energy expectation> immediately afterward remains $E_1^{\mathrm{old}}$, as seen from $\hbar^2\int|\psi'|^2/(2m)$; the measurement outcomes are $E_n^{\mathrm{new}}=n^2E_1^{\mathrm{old}}/4$.
The new <ground state> is $L^{-1/2}\sin(\pi x/(2L))$. Its overlap is $4\sqrt2/(3\pi)$, so
$$
\boxed{P_{\mathrm{new\ ground}}=\frac{32}{9\pi^2}\simeq0.360.}
$$
The discontinuity of the <derivative> at the former wall does not invalidate the finite quadratic-form expectation, although it matters when applying the differential <Hamiltonian> pointwise. <Adiabatic expansion> would instead keep the state in the ground level and reduce its <energy> by four.
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