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

There is a step barrier at x=0, V_0 > E

I am given:

ψi = e^i(kx−ωt) --->

ψr = R e^i(−kx−ωt) <---

ψt = T e^(−αx−iωt) --->

Part of question I am confused about: State the two boundary conditions satisﬁed by the wave function at x = 0 and hence find expressions for |R|^2 and |T|^2

2. Relevant equations

N/A

3. The attempt at a solution

I have already worked out an equation for alpha in the previous part.

ψ1 = ψi + ψr

ψ2 = ψt

I started to apply the conditions ψ1(0) = ψ2(0) to get 1 + R = T

and d/dx ψ1(0) = d/dx ψ2(0) to get ik - iRk = -αT

I solved the above to get R = (ik +αT) / ik with T = 1 + R etc

I understand that |R|^2 = R x R* and |T|^2 = T x T*

However I am told that T = 1 - R since these are probability coefficients. Do I solve with T = 1-R (probability coefficients) or T = 1+R (using ψ1(0) = ψ2(0))? I am confused which one to use and why.

Many thanks.

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# [Quantum mechanics] Step barrier |R|^2 and |T|^2

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