and Quantum Mechanical Tunneling

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Presentation transcript:

and Quantum Mechanical Tunneling Barrier Penetration and Quantum Mechanical Tunneling

The potential "barrier" defined …but what if we “turn it upside down”? This is a finite potential barrier. We’ve learned about this situation: the finite potential well… I II III U E -L/2 L/2 When we solved this problem, our solutions looked like this… What would you expect based on your knowledge of the finite box?

wave packet approaching a barrier

Pedagogical exercise: consider time independent case (pure momentum states) to the left of the barrier to the right of the barrier Instructive to consider the probability of transmission and reflection… R+T=1 of course…

Wavefunction for Square Barrier

Transmission Coefficient:

Transmission Coefficient for Arbitrary non-Square Barriers:

Application: alpha decay

Why does the half life vary more than the kinetic energy?

alpha decay U(r) r E R kinetic energy of escaping alpha particle Separation of centers of alpha and nucleus at edge of barrier 9.1 fm Height of barrier 26.4 MeV Radius at which barrier drops to alpha energy 26.9 fm Width of barrier seen by alpha 17.9 fm Alpha's frequency of hitting the barrier 1.1 x 10^21/s

Decaying Black Holes

Hawking Radiation Mass of Sun: 10^{66} years. Mass of billion tons, size of proton, only 10 billion years.