Quantum Show that the parity operator Π anti-commutes with the momentum operator p. Use this to show that [Π,T] = 0, where T = p^2/2m.

Consider a particle at a central potential that has an orbital angular momentum l = 2h and a spin s = h. %3D a) Find the energy levels with their respective degeneration, if the particle has a spin-orbit interaction as follows H40 = YL · Š, with y a constant.

ext cenb. Consider a system whose states are given in term of complete and orthonormal set of kets |1>, |2 >, [3 >,14 > as follows: 1 1p >= |1 > + 기2 > +2|3 > + 기4 > i 214> Where the kets |n > are eigenstates of an observable A defined on the system as follows: 2 A]n > = na|n > with n = 1,2,3,4 and with a a constant number. have 4) eiyen vealue 1. If A is measured, which values will be found and with which probabilities? 2. Find the expectation value of A for the state |Ø >. 3. Assume that the state 14> is found after the measurement of A. If A is measured again immediately, which states will be found and with which probabilities? 4. Find the expectation value of A if the system is in the state |4 >. 5. Assume B another observable defined on the system, which is compatible with A. Write the uncertainty inequality between A and B. 6. If B is measured, which states will be found and with which probabilities?

Show the relation LxL = iħL for the quantum mechanical angular momentum operator L