Question 3120marks] Consider a step potential with E>U. (Where U is the usual step-potential, V.) U=0 U X- x=0 (a) Exami

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Question 3120marks Consider A Step Potential With E U Where U Is The Usual Step Potential V U 0 U X X 0 A Exami 1 (32.5 KiB) Viewed 21 times

Question 3120marks] Consider a step potential with E>U. (Where U is the usual step-potential, V.) U=0 U X- x=0 (a) Examine the Schrodinger Equation to find the form of the solution in the region x ≤ 0, x>0 and complete the solution by applying the appropriate boundary equations. (12) (b) Obtain an expression for the reflection coefficient and show that R= where ki (k₂-k₂)² (k₁+k₂)²³ and k2 are wave numbers for the incident and transmitted waves, respectively. Also write 21₁ = . the transmission factor T'using the sum rule used by these coefficients. (c) Evaluate R and T in the limiting cases of EU and E → 00. Fou 40-20 R-> 1 T-oo (obsson) (5) (3)