$($a$)$ Calculate the expectation value of the kinetic energy for a particle $"$in a box" if it can occupy the two lowest states. That is$,$ assume the wave function to be given by

$2$

U$=$ C$1\backslash$tau$12$

U$1+$ C$2\backslash$tau$22$

U$2$ with C$1=$ C$2$

$($b$)$ Suppose that instead of C$1=$ C$2$ as in part $($a$),$ it is observed that the value of the kinetic energy of the particle is twice that of the lowest stationary state. What values of C$1$ and C$2$ would satisfy this observation?