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- Show that the minimum cnergy of a simple harmonic oscillator is Fw/2 if ArAp = h/2, where (Ap)² = ((p - (p))?). %3DView of a one-dimensional harmonic oscillator system on the x axis of a charged particle q with an energy spectrum of En = (n + ½)ħw. The system is then disturbed by an oscillating electric field as a wo• function of time t such that the disturbance potential energy can be expressed as untuk t o 0 v (t) = {_q {-9€x sin wt e-t With & electric field amplitude. (notes : untuk means for) a. Calculate the transition probability from state n to state m. b. State which transitions n → m are allowed and which are not allowed to occur. c. Explain what happens if w → wo and/or → 0. [Hint: Use the create and annihilate operators to enumerate Matrix elements.]Activity 7 (a) Solve the following equations for real x and- (i) 3+5i+x-yi = 6 – 2i (4*3 (ii) x+yi=(1-i)(2+8i). (b) Determine the complex number z which satisfies z(3+3i) = 2-i.