There are 2 questions related to Quantum Physics: PHY256. Please if you could help in handwriting not typed. That would be great. Thank you so much in advance.

4. Consider a particle of mass m in a 1D innite-potential square well of width 2L: Let it initially be in the ground state, and then the well is suddenly widened to 4L. (3) Calculate the probability of nding the particle in the l\"[ excited state of the widened well. (b) Does the particle have well-dened energy in the widened well (before any measurement)? Why? 5. Extra Credit: (a) Show that the position and momentum operators do not commute: [x, pl] E xpx - pxx i O. (b) Show that the time and energy operators do not commute: [t, E] E t E - E t a 0. Hint: Apply each commutation relation on a general 'P, using px E ih afx and E E +15 agar. Note: In Schrodinger quantum mechanics, position and time operators are just x and t respectively