It is known that animals cannot be explained using classical physics, since they tunnel through walls. The chickens thus exhibit quantum behavior and should be described with quantum mechanics.
The Schrödinger Equation gives us the behavior of wave function of the animal, which describes probabilistically how the animal will behave. According to the Born interpretation, describes the probability that the chicken will be at , but the exact outcome of the experiment cannot be known.
Estimation of mass of chicken
We know that chickens tunnel through 1m thick walls, so their De Broglie Wavelength should be on the order of 1m, and their speed is on the order of . We know that
Plugging our values in and with , we get
This shows us that the chickens are very very light.
Behaviour of chicken in pen
This problem requires that we know the Hamiltonian operator of our chicken pen, where is the potential of the pen, so we can solve the Schrödinger equation for this problem. We can assume that the potential is piecewise constant, zero inside the pen and outside (finite potential well model), so
Inside the pen
Inside the pen, we have . Plugging this into the Schrödinger equation gives us
Define . Since our problem is one-dimensional, we can solve this second-order differential equation with a function
for some constants
Outside the pen
Outside the pen, we have .
This is an excerpt of the upcoming book "Quantum Mechanics of Animals"