I can show that for a step potential and E < V, that the wave function is fully reflected and has no transmission into the potential interval (interval 2), x =0 at interval boundary, by(adsbygoogle = window.adsbygoogle || []).push({});

Wave equation for interval 1: Ψ_{1}= A_{1}e^{ik1x}+ B_{1}e^{-ik1x}

Wave equation for interval 2: Ψ_{2}= A_{2}e^{κ2x}

where B_{1}= A_{1}(k_{1}- iκ_{2})/(k_{1}+ iκ_{2})

and

A_{2}= A_{1}(2k_{1})/(k_{1}+ ik_{2})

Further B_{1}/A_{1}= (k_{1}- iκ_{2})/(k_{1}+ iκ_{2})

|B_{1}|/|A_{1}| = (k_{1}^{2}- iκ^{2}_{2})^{1/2}/(k^{2}_{1}+ iκ^{2}_{2})^{1/2}= 1

and |B_{1}| = |A_{1}| by which we can conclude full reflection.

However, if I calculate the reflection and transmission value by the probability current density, I find,

For interval 1

j_{1}x = ħk_{1}/m (|A_{1}|^{2}-|A_{1}|^{2}|ρ(E)|^{2})

where

|ρ(E)| = (k_{1}- iκ_{2})/(k_{1}+ iκ_{2})

But with this value for |ρ(E)| the probability current density in interval 1 does not match the probability current density of the incident wave, i.e.

j_{incident}x = ħk_{1}/m (|A_{1}|^{2})

But these must match for full reflection.

Not sure how I am getting this result.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Inconsistent Reflection and Transmission values-step potential & E < V

Loading...

Similar Threads for Inconsistent Reflection Transmission |
---|

B What is reflection? |

I Total reflection in Feynman picture |

B Reflection of light from the mirror |

**Physics Forums | Science Articles, Homework Help, Discussion**