A class of exactly solvable models to illustrate supersymmetry and test approximation schemes in quantum mechanics
Abstract
We derive the analytical eigenvalues and eigenstates of a family of potentials wells with exponential form (FPWEF). We provide a brief summary of the supersymmetry formalism applied to quantum mechanics and illustrate it by producing from the FPWEF another class of exact solutions made of their isospectral partners. Interestingly, a subset of the supersymmetric partners provides a class of exactly solvable double well potentials. We use the exact solutions of the FPWEF to test the robustness and accuracy of different approximation schemes. We determine (i) the ground state through variational method applied to an approriate set of trial functions and (ii) the whole spectrum using three semiclassical quantization formula: the WKB, JWKB and its supersymmetric extension, the SWKB quantization formula. We comment on the importance of Maslov index and on the range of validity of these different semiclassical approaches.
Read the paper
Related studies
- Comparative effectiveness of GLP-1 receptor agonists on glycaemic control, body weight, and lipid profile for type 2 diabetes: systematic review and network meta-analysis
- Adverse effects of cyclooxygenase 2 inhibitors on renal and arrhythmia events: meta-analysis of randomized trials
- Benefits and harms of drug treatment for type 2 diabetes: systematic review and network meta-analysis of randomised controlled trials
- Comparative effectiveness and safety of statins as a class and of specific statins for primary prevention of cardiovascular disease: A systematic review, meta‐analysis, and network meta‐analysis of randomized trials with 94,283 participants
- Screen time increases overweight and obesity risk among adolescents: a systematic review and dose-response meta-analysis
- Exposure to WHO AWaRe antibiotics and isolation of multi-drug resistant bacteria: a systematic review and meta-analysis
Go deeper in Evidence Hub
Evidence Hub adds a study data sheet (design, sample size, evidence level, key numbers), an AI summary and a chat grounded in the paper's text.