Consider a particle in an infinite box described by the following superposition state:

(x)=31(x)+42(x)

wheren are eigenstates(stationary states) of the Hamiltonian

a) Normalize (x).

b) What are the possible values/outcomes resulting from a measurement of the kinetic energy of a particle in an infinite box described by the wavefunction (x)? What are the probabilities to measure the different values of the kinetic energy?

c) What is the expected (average) value of the kinetic energy resulting from measuring this quantity many times?

d) What is the probability to find the particle in the first quarter of the box.