Estimate the ground state energy and wavefunction for a particle in a box using the variational method with the following trial wavefunction, where n is the normalization constant and β is a variational parameter that should be minimized. |ψ〉=nexp(−βx2) is this a good trial wavefunction for this approximation (justify your answer)? why is this not a good wavefunction? can you solve this problem both analytically and numerically?