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Problem 4 Time-dependent Schrodinger equation is of the form d4 a = A4 at Where a is a constant. a. Show that this equation has the following property. Let H be the Hamiltonian of a system composed of two independent parts, so that A(x1,x2) = A1 (x1) + A2(x2) And let the stationary states of system 1 be 41 (x1,t) and those of system 2 be 42 (x2,t). Then the stationary states of the composite system are 4(x1,X2, t) = 41(x1,t)42(x2,t) That is, show that this product forms a solution to the preceding equation for the given composite Hamiltonian. b. Show that this property is not obeyed by a wave equation that is second order in time, such as a2 a24 at² = A4

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