# Scattering on delta function potential

Suppose a particle has energy $E>V(+/-\infty)=0$, then the solutions to the Schrodinger equation outside of the potential will be $\psi(x)=Ae^{i k x}+Be^{-i k x}$. How can one show or explain that $|B|/|A|$ gives the probability that a particle scattering off the potential is reflected?

-
You can either argue with probability currents (though this was always confusing to me). The nice way is to construct wave-packets with the scattering solutions of a small range of momenta and then calculate what is the probability of the particle to be scattered. – Fabian Aug 31 '12 at 5:32
Can you explain more? If I start with a gaussian wavepacket, how do I get it to travel? If I apply the schrodinger equation to find its time evolution, it just stays at the same point but flattens out, how can I input its initial speed? – Hobo Sep 2 '12 at 15:55
@Hobo: work with the momentum first. Try something like $\int dk A\,e^{-\alpha k^{2}}e^{-i\beta kx}$, with $A, \alpha,$ and $\beta$ constant. – Jerry Schirmer Sep 2 '12 at 16:18

2
– jjcale Sep 2 '12 at 16:55
@jjcale: voted to close as duplicate, I can't see how to answer without replicating the answer to the previous question verbatim. – Ron Maimon Sep 2 '12 at 21:48
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 6, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "english_confidence": 0.918846607208252, "perplexity_flag": "head"}