Question

JO) A Pi- electron in benzene molecule may be described in quantum com make the assumption that benzene is circular. In such a case, the potential energy is constant (1.e. V =0) and Schrodinger equation for a particle of mass me constrained to move on a circle of radius a is: (-h7/8 Tma)dade - Em for 0 SOS 27. Here is the angle that describes the position of the particle (i.e. pi-electron) around the ning a) Show that the solution to this equation is oo) = N eine where n = (8 ma-E)"/h and N is the normalization constant. b) Derive an expression for energy, E in terms of n, m, a and h only above. e) Show that the normalization constant N = (270-12 for the function or

Answer 1

E4 81mat dl marE ф —о (8114marB + rip thigerural sduhan is, (0)e OP SS C pco)- ee) Thun fm en2 D&we gu in Hne the sduten nce)= Neme Ahre Nisthe normaluttu comtam NoW Wehev 81mat E h4 TmatE = 4 E 71mar Pasible valuesof m fom the simgle valutdnuo crteria (a1+0) 0) Nenten+0)Neine

in =1 0 2,.---- E () c0)Nein @. NoYmalta tuon cmdeton T 2 e 4D1 N N TT 7. NS 2 IT - Normaltatn tontam N= Thue co) heino With n=9キリは2-