Hello,(adsbygoogle = window.adsbygoogle || []).push({});

As a path-integral newbie, I've been trying to calculate the amplitude for an electron which enters a box (potential within the box is given) at a point to emerge the other edge of the box (it doesn't matter when it exits). For simplicity, I first tried to work out the problem in one dimension, and in discrete space-time. To simplify it even further, I tried with a constant (but non-zero) potential.

I worked out the kernel [tex]K(b,a)[/tex], but it -naturally- depends on time spent in the "box". But I don't carewhenwill exit, I care only whether if it can or can not penetrate through.

I have [tex]\psi(b,t_b) = \int K(b,a) \psi(a,t_a) da[/tex], and transmission amplitude at [tex]t_b[/tex] would be "inner product" of wavefunctions at [tex]t_b[/tex] and [tex]t_a[/tex] (but well, how? They don't have a variable in common at all! Do I get to expand the wavefunction in eigenstates of position?). So I guess, to get the total amplitiude, I get to compute the amplitude for all times after [tex]t_a[/tex], and add them all. Sounds plausible to me, but how would I do an inner product with [tex]\psi(b,t_b)[/tex] and [tex]\psi(a,t_a)[/tex]? Or am I quite off?

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

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!

# Transmission amplitude using path-integrals

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

Loading...

Similar Threads - Transmission amplitude using | Date |
---|---|

B Can heating/cooling a material effect absorption, and transmission | May 6, 2016 |

B If you raise the electron to other higher shell states, can it affect light transmission? | Feb 2, 2016 |

Transmission Line Model (TLM) End Resistance (Re) | Dec 11, 2015 |

What is an approximate amplitude of a phonon? | Oct 30, 2015 |

Does tunneling transmission probability depend on the density of states or velocity? | Sep 28, 2014 |

**Physics Forums - The Fusion of Science and Community**