Quantum Mechanical Tunneling - Wilfrid Laurier University量子力学隧道效应-劳里埃大学.pdf

Quantum Mechanical Tunneling The square barrier: Behaviour of a classical ball rolling towards a hill (potential barrier): If the ball has energy E less than the potential energy barrier (U=mgy), then it will not get over the hill. The other side of the hill is a classically forbidden region. Quantum Mechanical Tunneling The square barrier: Behaviour of a quantum particle at a potential barrier Solving the TISE for the square barrier problem yields a peculiar result: If the quantum particle has energy E less than the potential energy barrier U, there is still a non-zero probability of finding the particle classically forbidden region ! This phenomenon is called tunneling. To see how this works let us solve the TISE … Quantum Mechanical Tunneling The square barrier: Behaviour of a quantum particle at a potential barrier To the left of the barrier (region I), U=0 Solutions are free particle plane waves: 2mE (x ) = Aeikx + Be ikx , k = The first term is the incident wave moving to the right The second term is the reflected wave moving to the left. 2 ref lected B 2 Reflection coefficient: R = = 2 2 incident A Quantum Mechanical Tunneling The square barrier: Behaviour of a quantum particle at a potential barrier To the right of the barrier (region III), U=0. Solutions are free particle plane waves: 2mE (x ) = Feikx , k = This is the transmitted wave moving to the right Transmission coefficient: 2 2 transmitted F T =