For the following system use matlab to calculate the

Question

Problem 1: Multiple barriers

For the following system, use Matlab to:

1. Calculate the coefficients A' of ?? after two finite barriers via transfer matrix approach

2. Calculate transmission probability (T=|A'|²/|A|²) in case of E>V

Choose E = 4 eV, V = 2 eV, a = 0.1 nm, b = 0.3 nm

Problem 1: Multiple barriers

• Penetration-though-barriers problem can be found in many quantummechanics textbooks. Here I attached the second chapter from Atkin's book Molecular Quantum Mechanics (I think the book is very clear). Section 2.10 is directly relevant to it.
• The transfer matrices can be derived, or you can refer to the scanned pages of Gilmore's book Elementary Quantum Mechanics in One Dimension (I've highlighted the most useful parts, in page 13~17)
• There're four breakpoints between region 0 to 4, and thus four matrix transformations in this system. Pay attention to the last transformation, where the coefficient B' is set to be 0
• Coefficient A could be set as 1 during numerical calculation, as transmission probability is only a ratio.

Problem 2: Inelastic tunneling-electronic coupling

For the following system, use Matlab to calculate transmission probability (T=|C|²/|A|²) of ??1 solving a system of linear equations of variables A, B, C, B' and C'

Choose E = 4 eV, V1 = 1 eV, V2 = 3 eV, W = 6

 

 

Attachment:- _5279377 1 Problems-2.pdf