5. Consider a potential barrier represented as follows: U M 0 +a U(x) = x a Determine the transmission coefficient as a function of particle energy.

View 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.]

For the potential-energy functions shown below, spanning width L, can a particle on the left side of the potential well (x 0.55L)? If not, why not? b. c. 0 a. 0o 00 E E E-