At t = 0 , the wavefunction of an otherwise free particle confined between two infinite walls at x = 0 and x = L is ψ(x, t = 0) = \(\sqrt{\frac{2}{L}}\left(\sin \frac{\pi x}{L}-\sin \frac{3 \pi x}{L}\right)\). Its wave function at a later time \(t=\frac{m L^2}{4 \pi h}\) is
1
\(\sqrt{\frac{2}{L}}\left(\sin \frac{\pi x}{L}-\sin \frac{3 \pi x}{L}\right) e^{i \pi / 6}\)
2
\(\sqrt{\frac{2}{L}}\left(\sin \frac{\pi x}{L}+\sin \frac{3 \pi x}{L}\right) e^{-i \pi / 6}\)
3
\(\sqrt{\frac{2}{L}}\left(\sin \frac{\pi x}{L}-\sin \frac{3 \pi x}{L}\right) e^{-i \pi / 8}\)
4
\(\sqrt{\frac{2}{L}}\left(\sin \frac{\pi x}{L}+\sin \frac{3 \pi x}{L}\right) e^{-i \pi / 8}\)
5
Question Not Attempted