Solving schrodinger, reflection coefficientby SoggyBottoms Tags: coefficient, reflection, schrodinger, solving 

#1
Mar712, 11:39 PM

P: 61

Consider the potential
[tex] V(x) = \begin{cases} 0, & x < a & (I) \\ +W, & a < x < a & (II) \\ 0, & x > a & (III) \end{cases} [/tex] for a particle coming in from the left ([itex]\infty[/itex]) with energy E (0 < E < W). Give the solution to the Schrodinger equation for I, II and III and use these to calculate the reflection coefficient. I have the answer to this problem in front of me, but I don't understand. First they calculate the solution to the Schrodinger equation for I, II and III: [itex]\psi_I(x) = Ae^{ikx} + Be^{ikx}, \ \mbox{with} \ k = \frac{\sqrt{2mE}}{\hbar}[/itex] [itex]\psi_{II}(x) = Ce^{\kappa x} + De^{\kappa x}, \ \mbox{with} \ \kappa = \frac{\sqrt{2m(E  W)}}{\hbar}[/itex] [itex]\psi_{III}(x) = Fe^{i k x}, \ \mbox{with} \ k = \frac{\sqrt{2mE}}{\hbar}[/itex] I understand [itex]\psi_I[/itex], but not [itex]\psi_{II}[/itex] and [itex]\psi_{III}[/itex]. Why is there no i in [itex]\psi_{II}[/itex]? And why is [itex]\psi_{III}[/itex] only a single term? I imagine it has something to do with the particle coming from the left? 



#2
Mar812, 12:30 AM

Sci Advisor
P: 2,194





#3
Mar812, 10:31 AM

P: 61





#4
Mar812, 05:31 PM

Sci Advisor
P: 2,194

Solving schrodinger, reflection coefficient 



#5
Mar812, 11:36 PM

P: 61

Thanks!



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