The infinite well and Dirac delta function potentials as pedagogical, mathematical and physical models in quantum mechanics

DOI10.1016/j.physrep.2014.02.005zbMath1357.81080OpenAlexW2041174349MaRDI QIDQ516860

Yong-Cai Geng, Sumit K. Garg

Publication date: 15 March 2017

Published in: Physics Reports (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physrep.2014.02.005

zbMATH Keywords

quantum mechanicsDirac delta functioninfinite well

Mathematics Subject Classification ID

History of mathematics in the 20th century (01A60) History of quantum theory (81-03) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05)

Related Items (26)

Using zero-energy states to explore how external boundaries affect the number of bound states in a quantum well ⋮ Optimal strategies to infer the width of an infinite square well by performing measurements on the particle(s) contained in the well ⋮ Nonlocally induced (fractional) bound states: Shape analysis in the infinite Cauchy well ⋮ Bounded solution structure of Schrödinger equation in the presence of the minimal length and its effect: bound states in the continuum are universal ⋮ On scattering from the one-dimensional multiple Dirac delta potentials ⋮ The infinite square well potential in momentum space ⋮ Dimensional analysis and the correspondence between classical and quantum uncertainty ⋮ Fractional Schrödinger equation with Riesz-Feller derivative for delta potentials ⋮ Quantum Information Measures of the One‐Dimensional Robin Quantum Well ⋮ Asymmetric quantum wells and the solotone effect: towards an inverse method ⋮ Hyperspherical \(\delta\)-\(\delta'\) potentials ⋮ Constrained quantum motion in \(\delta\)-potential and application of a generalized integral operator ⋮ Evolution of electric-field-induced quasibound states and resonances in one-dimensional open quantum systems ⋮ On the ambiguous treatment of the Schrödinger equation for the infinite potential well and an alternative via singular potentials: the multi-dimensional case ⋮ Nonlinear Schrödinger equation with a Dirac delta potential: finite difference method ⋮ The 3D perturbed Schrödinger Hamiltonian in a Friedmann flat spacetime testing the primordial universe in a non commutative spacetime ⋮ Propagator calculations for time dependent Dirac delta potentials and corresponding two state models ⋮ Some Recent Results on Contact or Point Supported Potentials ⋮ Stability results for discontinuous nonlinear elliptic and parabolic problems with a S-shaped bifurcation branch of stationary solutions ⋮ Measuring the practical particle-in-a-box: orthorhombic perovskite nanocrystals ⋮ The Lippmann–Schwinger Formula and One Dimensional Models with Dirac Delta Interactions ⋮ Bound and scattering states for supersingular potentials ⋮ Threshold scattering for the focusing NLS with a repulsive Dirac delta potential ⋮ Comb-like geometric constraints leading to emergence of the time-fractional Schrödinger equation ⋮ Fractional Schrödinger equation for heterogeneous media and Lévy like distributions ⋮ Brownian motion in trapping enclosures: steep potential wells, bistable wells and false bistability of induced Feynman–Kac (well) potentials

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