The time-independent Schrodinger equation with Dirac delta potentials in an infinite potential well

The infinite potential well is one of the most well-known models in quantum mechanics, as well as the Dirac delta potential. In the first part of the thesis, one Dirac delta potential is considered using the time-independent Schr"{o}dinger equation, the typical boundary conditions for an infinite well and normalization conditions to obtain the wave function $\psi(x)$. The system naturally imposes an additional condition at $\psi(0)$ due to the Dirac delta function, which yields the final equation for the energy levels $\{E_n\},$ that has infinitely many solutions. In the second part, a lattice potential within the infinite well is considered, which is defined as a finite sum of Dirac delta functions that are spread evenly within the bounds of the well. For future work, more numerical analysis should be done on these systems, as well as expanding the problem to several dimensions.