The quantum behavior of a particle in a square well of finite, uni-dimensional potential. The entangled fate of Schrödinger’s cat.

Abstract
An in depth look to the quantum behavior of a particle in a unidimensional finite, square box of potential energy is presented. Wave function normalization constants are fully determined and are used to establish an expression to calculate the particle allowed energy eigenstates based in the confinement condition for each of the two possible wave function symmetries. These eigenstates turn out to be degenerate and it becomes possible to configure confined systems so that the particle confinement/near free duality condition, also known as entanglement is present. This condition, obtained by using the particle mean presence probability density function of the two wave function symmetries of the system degenerate states, is illustrated with a couple of calculation examples.

Keywords
Quantum system, degenerate eigenvalues, entanglement, Rydberg unit of energy

Cite this paper
Emmanuel Saucedo-Flores, The quantum behavior of a particle in a square well of finite, uni-dimensional potential. The entangled fate of Schrödinger’s cat. , SCIREA Journal of Physics. Volume 6, Issue 4, August 2021 | PP. 61-75. 10.54647/physics14337

References

[ 1 ]	Finite Square Well. (2020, May 5). Tom Weideman, University of California, Davis Last retrieved May 25, 2021, from https://phys.libretexts.org/@go/page/17175
[ 2 ]	One Dimensional Finite Depth Square Well. Michel Fowler, University of Virginia Last retrieved May 26, 2021, from http://galileo.phys.virginia.edu/classes/252/FiniteSquareWell/FiniteSquareWell.html
[ 3 ]	Particle in a Finite Square Potential Well. 2013-04-08. Richard Fitzpatrick, University of Texas. Last retrieved May 10, 2021, from https://farside.ph.utexas.edu/teaching/315/Waveshtml/node96.html
[ 4 ]	Finite Potential Well. Last retrieved May 20, 2021, from https://en.wikipedia.org/wiki/Finite_potential_well