# What types of particles have a higher probability of tunnelling?

1. May 23, 2012

### idea2000

Hi,

This is a really basic question that I was hoping to get a simple answer for. What types of particles tunnel the most effectively? Do high energy electrons tunnel more effectively than if they were at low energy?

2. May 24, 2012

### Khashishi

The probability for tunneling depends on the amplitude of the wavefunction in the potential barrier. The wavefunction drops off exponentially in the barrier region. Looking at Schrodinger's equation
$\frac{d^2}{dx^2}\Psi(x)=\frac{2m}{\hbar^2}(V(x)-E)\Psi(x)$
for constant V > E we get solutions like
$\Psi(x) = A e^{-\kappa x} + B e^{\kappa x}$
$\kappa^2 = \frac{2m}{\hbar^2}(V-E)$
The penetration depth goes as $1/\kappa$, so we have more tunneling when mass and V-E are low compared to hbar^2.