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

A particle with the energy E < V[itex]_{0}[/itex] (V[itex]_{0}[/itex] > 0) moves in the potential V(x) = 0, x<0 ; V(x)= V[itex]_{0}[/itex], 0<x<d and V(x)= 0, x>d. Measure the probability that the particle will tunnel through the barrier by calculating the absolute value of the ratio squared, |[itex]\Psi[/itex](d)/[itex]\Psi[/itex](0)|[itex]^{2}[/itex] between the values of the wave function at x=d and x = 0

Calculate the probability for anelectron, when V[itex]_{0}[/itex]- E=1 eV and d = 1 Å.

2. Relevant equations

[itex]\Psi[/itex](x) = ae[itex]^{\kappa*x}[/itex]+be[itex]^{-\kappa*x}[/itex], [itex]\kappa[/itex] = [itex]\sqrt{2m( V_{0}-E)/\hbar^{2}}[/itex] for E<V[itex]_{0}[/itex]

3. The attempt at a solution

Firstly I get:

[itex]\kappa[/itex] = [itex]\sqrt{2m(1)/\hbar^{2}}[/itex] for E<V[itex]_{0}[/itex]

However, the problem is with this wave function:

[itex]\Psi[/itex](x) = ae[itex]^{\kappa*x}[/itex]+be[itex]^{-\kappa*x}[/itex]

In order to calculate the ratio, |[itex]\Psi[/itex](d)/[itex]\Psi[/itex](0)|[itex]^{2}[/itex], I think I have to defineaandbsomehow, but I don't know where to start.

Thanks!

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

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!

# Homework Help: Probability for Quantum tunnelling

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