11 research outputs found
Introduction to Gauge Theory of Gravitation
The fundamental interactions of nature, the electroweak and the quantum
chromodynamics, are described in the Standard Model by the Gauge Theory under
internal symmetries that maintain the invariance of the functional action. The
fundamental interaction of gravitation is very well described by Einstein's
General Relativity in a Riemannian spacetime metric, but General Relativity has
been over time a gravitational field theory apart from the Standard Model. The
theory of Gauge allows under symmetries of the group of Poincar\'e to impose
invariances in the functional of the action of the spinor field that result in
the gravitational interaction with the fermions. In this approach the
gravitational field, besides being described by the equation similar to General
Relativity, also brings a spin-gravitational interaction in a Riemann-Cartan
spacetime.Comment: 23 page
Solution of the 1d Schrödinger Equation for a Symmetric Well
We suggest a mathematical potential well with spherical symmetry and apply to the 1d Schrödinger equation. We use some well known techniques as Stationary Perturbation Theory and WKB to gain insight about the solutions and compare them each other. Finally, we solve the 1d Schrödinger equation using a numerical approach with the so-called Numerov technique for comparison. This can be a good exercise for undergrad students to grasp the above cited techniques in a quantum mechanics course