(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

a particle of kinetic energy E is incident from left on a potential barrier,height U, situated at the origin.the barrier is infinitely wide and E>U

obtain an expression for the reflection coefficient R of the particle as a fuction ratio e=E/U

2. Relevant equations

3. The attempt at a solution

to left of barrier wavefunctions are free particle waves

barrier at x=0

psi(x,t)=Aexp(ikx-wt)+ Bexp(-ikx-wt) x<0

within barrier wavefunction also is oscillatory

E=h(cross)*w

considering case for E<U and using TISE on psi(x,t) within barrier we get

a=([2m(U-E)]^0.5)/h(cross)

but now E>U and as a result a becomes imaginary. introducing new wavenumber L and barrier wavefunction becomes

psi(x,t) =Cexp(-iLx-wt)+Dexp(iLx-wt) x>0 (note this is equation is only for a barrier of finite width)

but now everywhere to right from origin x=0 is the barrier wavefunction given above . to keep psi(x,t) from diverging for large x we must take D=0 leaving only decaying wave and this is where i am up to i was just wanting to know if i am on the right track

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# Homework Help: Potential barrier problem

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