(IV) Consider a superposition 4+(x, t) of a particle in an infinite 10 unit well, which is positioned symmetrically around zero (sis ). Assume the superposition Y+(x) is equally composed by the ground state and first excited state at time t = 0, 0+(2) = avi(2) + a02(2), where a are real positive numbers that guarantee the proper normalization and enforce that V+(x) has indeed equal contributions of both 41(2) and 42(2). (Hint: see the lec- ture!) What's the expectation value of at t = 0? With the time evolution operator, the superposition evolves dependent on time, U+(t) = e-t, *++(t = 0) 0 t41(,t) = = Note that the Hamiltonian in the exponent will act on an eigenstates Vi as: e E F2+41(1,1), where E1 is the energy 01. What will be the expectation value of position operator at t = Ej, assuming E1 is the eigenenergy for the ground state? E1 2 (IV) Consider a superposition 4+(x, t) of a particle in an infinite 10 unit well, which is positioned symmetrically around zero (sis ). Assume the superposition Y+(x) is equally composed by the ground state and first excited state at time t = 0, 0+(2) = avi(2) + a02(2), where a are real positive numbers that guarantee the proper normalization and enforce that V+(x) has indeed equal contributions of both 41(2) and 42(2). (Hint: see the lec- ture!) What's the expectation value of at t = 0? With the time evolution operator, the superposition evolves dependent on time, U+(t) = e-t, *++(t = 0) 0 t41(,t) = = Note that the Hamiltonian in the exponent will act on an eigenstates Vi as: e E F2+41(1,1), where E1 is the energy 01. What will be the expectation value of position operator at t = Ej, assuming E1 is the eigenenergy for the ground state? E1 2