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What types of particles have a higher probability of tunnelling?

  1. May 23, 2012 #1
    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. jcsd
  3. May 24, 2012 #2
    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
    [itex]\frac{d^2}{dx^2}\Psi(x)=\frac{2m}{\hbar^2}(V(x)-E)\Psi(x)[/itex]
    for constant V > E we get solutions like
    [itex]\Psi(x) = A e^{-\kappa x} + B e^{\kappa x}[/itex]
    [itex]\kappa^2 = \frac{2m}{\hbar^2}(V-E)[/itex]
    The penetration depth goes as [itex]1/\kappa[/itex], so we have more tunneling when mass and V-E are low compared to hbar^2.
     
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