A particle of mass m is confined in the ground state of a one dimensional box extending from x = −2L to x = +2L . The wave function of the particle in this state is \(\rm ψ(x)=ψ_0\cos\left(\frac{\pi x}{4L}\right)\) where ψ0 is a constant. The energy eigenvalue corresponding to this state is
1
\(\rm \frac{\hbar^2 \pi^2}{32 mL^2}\)
2
\(\rm \frac{\hbar^2 \pi^2}{2 mL^2}\)
3
\(\rm \frac{\hbar^2 \pi^2}{4 mL^2}\)
4
\(\rm \frac{\hbar^2 \pi^2}{16 mL^2}\)