Consider the reflection and transmission of a left-incident current of particles at the potential 0 for x0 V (r) _ Vo for x>0 Proceed along the following lines: (a) Solve the stationary Schrödinger equation separately in the two regions and 0 for an energy E > Vo. 0 (b) Sketch the potential and indicate with arrows which parts of the solutions you got in (a) to zero, so that the remaining three represent a right-moving incident wave and a left-moving reflected wave in the region x < 0, and a right-moving transmitted wave in the region x > 0. are left- moving and which are right-moving. Set one of the coefficients (c) Calculate the incident, reflected, and transmitted currents, and find expressions for the reflection probability R T jirans/jinc (Watch out here!. T comes out differently than in the example we did in the lecture.) jrefi/in and the transmission probability (d) Impose the continuity of o and ôø/dx at the boundary equations you get to calculate R and T. Find RT (If you get anything other than 1 for the sum of reflection and transmission probabilities, check your calculation again and find the mistake you have made.) 0, and use the two (e) Give R and T as functions of E. (Only the ratio E/Vo matters, and m and h should drop out.)

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