Fiol Núñez, BartomeuVega Casanovas, Andreu2025-09-232025-09-232025-06https://hdl.handle.net/2445/223364Treballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Curs: 2025, Tutor: Tomeu Fiol NúñezThis work investigates attractive potentials of the form 1/rN for N ≥ 2 in Quantum Mechanics. For the inverse square potential (N = 2) with sufficiently strong coupling, we examine how classical scale symmetry is broken through the renormalization process, representing the simplest example of a quantum anomaly and touching upon the fundamental question of what symmetries are present in reality. This anomaly is exemplified by the existence of a critical dipole moment required to bind an electron to a polar molecule. In contrast, singular potentials with N > 2 exhibit stronger divergences, and we argue why a complete theory cannot be recovered with finitely many parameters, drawing an analogy with nonrenormalizable theories in quantum field theory9 p.application/pdfengcc-by-nc-nd (c) Vega, 2025http://creativecommons.org/licenses/by-nc-nd/3.0/es/Trencament de simetriaInvariància d'escalaTreballs de fi de grauSymmetry BreakingScale invarianceBachelor's thesesinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess