3 Consider a particle, of mass m, in a box (infinite square well) with walls at x = 0 and x = a. Initially the particle had a constant wave function in the left half of the box (I e 0 to a/2). Work out the probability that energy measurement will yield the ground state energy (I e n=1, lowest energy).
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- A particular two-level quantum system has two eigenstates given by Ig) := (9) le) := (¿) where |g) is the ground state and le) is the excited state. The Hamiltonian operator is given by Îû = () O A a. Write down the density matrix and calculate for the partition function. b. Calculate for the mean energy of the system. c. Calculate for the expectation value of the operator 1 0 0-134. a) Consider a square potential well which has an infinite barrier at x = 0 and a barrier of height U at x = L, as shown in the figure. For the case E L) that satisfy the appropriate boundary conditions at x = 0 and x = o. Put the appropriate conditions on x = L to find the allowed energies of the system. Are there conditions for which the solution is not possible? explain. U E L.