The Flash quantum tunneling vibration problem.

[jetwaterluffy]

I was reading "The physics of superheroes", and it mentioned The Flash being able to increase his kinetic energy to tunnel though walls. I tried to find out how fast he would have to go, assuming he is vibrating (as shown in the actual comic) so will have several tries at trying to tunnel though a wall. I will assume no relativity, as it will make the equations harder and may make the feat impossible. This is how far I have got so far:
P=e^-2KL
L= length of barrier. Let's assume a wall is 0.04m thick.
K= wave number =(sqrt(2m(V-E)))/h
m= mass. Let's say he weighs 80kg.
E= the flash's energy=mv²
v= Velocity. What I want to find out.
V= potential energy of the barrier. I have no idea what the potential energy of a brick wall is, so need your help on this.
h= Plank constant divided by 2pi= 1.06x10^-34 Js
P= Probablity necessary to tunnel = 4a/vt (I think).
a= amplitude of the flash's vibration. Let’s assume 0.005m.
t= Tunneling time. Let’s say he wants to get through in 0.1s.
So I have so far:
0.02/0.1v=e^{-2*0.04*((sqrt(2*80*(V-(80v2))))/1.06x10-34)}
0.2v^-1=e^{-0.08*((12.6*sqrt(V-(80v2))/1.06x10-34)}
0.2v^-1=e^{-0.08*1.19x1035*(V-80v2)}
0.2v^-1=e^{-9.52x1033*(V-80v2)}
I can't work out the potential energy of a brick wall, and would struggle solving the exponential. Can you help?

 

[azntoon]

The potential energy of a wall depends on the materials it is made from and the forces acting on it. It would be difficult to calculate the exact potential energy of a particular wall without knowing its exact composition and the forces acting on it. However, for the purposes of this problem, we can assume that the potential energy of the wall is significantly greater than the kinetic energy of The Flash. This simplifies the equation to:0.2v-1=e-9.52x1033*(V-80v2)=> 0.2v-1=e-9.52x1033*V=> v= (1+e^(9.52x1033)*V) / 0.2Therefore, to tunnel through the wall in 0.1s, The Flash would have to move at a velocity of (1+e^(9.52x1033)*V) / 0.02 m/s.