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. The inherentsensitivity of the Tunneling process can be exploited to produce photographsof individual atoms using scanning Tunneling microscopes (STM) or produceextremely rapid amplifiers using Tunneling diodes. It is an area of physics whichis as philosophically fascinating as it is technologically of this chapter deals withcontinuumrather than bound state bound state problems, one is usually concerned with solving for possible sta-tionary state energies.

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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  Functions, Density

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