Question

2. Consider the following approximation for a long conjugated molecule, where there is a flat potential across the conjugated region, and a harmonic oscillator like potential on either end. mwx2 2 if x < 0 m(x -a)2 if a<x ) Uhe the WKB mcthod to find the eneesnoting thar we hate no verticl wall. Yyou may want to shift the question to simplify the calculation. b) Does this give the exact answer as a → 0? Compare how this model behaves as a increases with the behaviour of the particle-in-a-box model as a increases. c) We might expect the space between the edges to have a periodic potential (representing each atom of the long molecule). Without calculating the energies, how would you think they would be affected?

Answer 1

v(x) = {1/2 mwx^2 1/2 mw(x - a)^2 if x < 0 if 0 < x < xa if a < x To find the energies Given xy = 2 y = 2/x, Notequalto 0, for energy x elementof rightarrow so, it is true Given xy = z x = 2/y, y Notequalto 0 y Notequalto 0 r alpha, it should not for Forall y elementof R it should be an false. \r\n Given xy = 2 for a particular value of x and y. To satisfy the relation like x = 1/2, y = 2 {so, many values} y = 2, x = 1 so, But you take only given two option to discus only (1) is correct. Only (2) is correct {in our screen