Transcription of Quantum Tunneling
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Quantum Tunneling
Quantum TunnelingIn this chapter, we discuss the phenomena which allows an electron to quan-tum tunnel over a classically forbidden eV9 eV99% of timeRolls over10 eV1% of the time10 eVRolls backThis is a strikingly non-intuitive process where small changes in either theheight or width of a barrier create large changes the Tunneling current of particlescrossing the barrier. Quantum Tunneling controls natural phenomena such asradioactive decay where a factor of three increase in the energy released duringa decay is responsible for a 1020fold increase in the decay rate.
current density, the wave function must have a position dependent phase. Otherwise, the phase of Ψ(x,t) will be the same as the phase of ∇~Ψ(x,t) and therefore Ψ∗∇~Ψ will be real. The current density for an electron in a stationary state of the form Ψ(x,t)=ψ(x) exp(−iωt) is zero since the phase dependence has no spatial dependence.
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