18. In differential form, what is the kinetic energy operator equal to? Does this depend on the problem that you are solving in quantum mechanics? What is the eigenvalue spectrum for this operator?

Solution 18. The expression for the kinetic energy can be written as the following: K=12mv2 =12m×mmv2 =12×mv2m =P22mTherefore, the kinetic energy operator is given by, K^=12mP^x2Substitute the momentum operator P^ above.P^x=-i♄∂∂xK^=12m-i♄∂∂x2 =12m-♄∂2∂x2 =-♄2m∂2∂x2 The operator is independent of the given problem. The eigenvalue spectrum of this operator is the set of the calculated eigenvalue of the kinetic energy operator for the given wavefunction.

Answered: 18. In differential form, what is the…