glaHHg, did a pretty good job explaining it. Except his discription of a potential barrier I believe is wrong. I think he was thinking of an infinite potential well.
I'm not a Physicist, but I'm an EE student and we covered this in properties of materials which is just another name for Quantum Physics for EE students.
A potential well graph looks like a line that is flat at some PE (potential energy) then goes down to a PE of 0 and then back up to the same hight as before. An infinite potential well has a PE of infinity at the top. In my class we dealt with electrons in a potential well. Inside the well V=0 and outside V=infinity. The electron is confined to the region 0 < x < a. Outside the region 0 < x < a the probablity of finding the electron per unit volume is 0 and inside it is given by Schrodinger's equation.
[edit: oops, the probability above is the square of the magnitude of Schrodinger's equation. Noticed my typo when I reread the posts above.]
To describe tunneling (aka quantum leak) I will look at it using an electron (because I'm EE). In the region 0 < x < a, the electron is moving with an energy E and since inside the potential well the PE is 0, E must be entirely made up of KE (Kinetic energy). When the electron encounters a potential barrier of "hight" V0, which is greater than E at a = 0. The width of the potential barrier is given by b. On the other side of the barrier (a + b) the PE is also 0.
Each of the three areas 1) left side of barrier x < a, 2) barrier a < x < a + b, and 3) right side of barrier x > a + b have a wavefunction given by Schrodinger's equation
psi1(x) = A1 exp(jkx) + A2 exp(-jkx)
psi2(x) = B1 exp(alpha*x) + B2 exp(-alpha*x)
psi3(x) = C1 exp(jkx) + C2 exp(-jkx)
where:
k^2 = 2mE/h-bar^2
The probability of tunneling through is given by:
T = T0 * exp(-2(alpha)b).
where:
T0 = ( 16 * E (V0 - E) ) / V0^2
alpha^2 = 2m (V0 - e)/h-bar^2
Both k and alpha are positive numbers.
The probability of reflextion is given by the Reflection coefficient:
R = A2^2/A1^2 = 1 - T
Hope this helps. I'm not a quantum physicist so take everything I say with a large grain of salt. I'm pretty sure it's correct though.
