Quantum Mechanics of a Particle in a Potential Well
Textbooks
Griffiths, D. J., & Schroeter, D. F. (2018). Introduction to Quantum Mechanics (3rd ed.). Cambridge: Cambridge University Press.
(See Chapter 2: “Time-Independent Schrödinger Equation”, section “The Infinite Square Well”, and later sections on finite wells.)Shankar, R. (2012). Principles of Quantum Mechanics (2nd ed.). New York: Springer.
(Chapter 5 treats bound states in one dimension, including infinite and finite square wells and their eigenvalues/eigenfunctions.)Sakurai, J. J., & Napolitano, J. J. (2020). Modern Quantum Mechanics (3rd ed.). Cambridge: Cambridge University Press.
(Introduces one-dimensional wells as examples of bound states and stationary solutions of the Schrödinger equation.)Cohen-Tannoudji, C., Diu, B., & Laloë, F. (1991). Quantum Mechanics (Vol. 1). New York: Wiley–VCH.
(Includes detailed analysis of particles in one-dimensional potentials, including square wells and barriers.)Gasiorowicz, S. (2003). Quantum Physics (3rd ed.). Hoboken, NJ: John Wiley & Sons.
(Chapters on one-dimensional potentials cover infinite and finite wells and their spectra.)Zettili, N. (2009). Quantum Mechanics: Concepts and Applications (2nd ed.). Chichester: John Wiley & Sons.
(Chapter on “Bound States in One Dimension” treats the infinite square well and finite potential wells extensively.)OpenStax. (2016). University Physics Volume 3. Houston: OpenStax.
See Section “7.4 The Quantum Particle in a Box”, which derives the wavefunctions and energies for a particle in a one-dimensional infinite well and discusses quantization.Ghatak, A. K., & Lokanathan, S. (2004). Quantum Mechanics: Theory and Applications (5th ed.). Macmillan Publishers India Limited.
(Chapter 6: Bound state solutions of the solution equation Schrödinger Equation)
Online Texts and Notes
OpenStax. (2016). “7.4 The Quantum Particle in a Box.” In University Physics Volume 3. Houston: OpenStax.
Available at: https://openstax.org/books/university-physics-volume-3/pages/7-4-the-quantum-particle-in-a-box
(Derives (E_n = \frac{n^2 h^2}{8mL^2}) and discusses zero-point energy and probability densities.)Physics LibreTexts. “The Infinite Potential Well.” In General Physics (UCD Physics 7C).
(Discusses boundary conditions, standing wave solutions, and quantized energies.)Wikipedia. “Particle in a Box.” The Free Encyclopedia.
(Covers the one-dimensional infinite well, extensions to 2D and 3D, and applications such as quantum dots, with formula (E_n = \frac{h^2 n^2}{8mL^2}).)Wikipedia. “Potential Well.” The Free Encyclopedia.
(General concept of potential wells in classical and quantum contexts.)Wikipedia. “Quantum Well.” The Free Encyclopedia.
(Applies the particle-in-a-box model to semiconductor quantum wells, including boundary conditions and energy levels.)Chemistry LibreTexts. “Particle in a 1-Dimensional Box.”
(Introductory yet mathematically explicit derivation used in physical chemistry courses, emphasizing quantization and probability distributions.)
University Lecture Notes / Supplements
Kurur, N. “Particle in an Infinite Potential Well.” Department of Chemistry, IIT Delhi.
(Lecture notes deriving eigenfunctions and quantized energies for a 1D infinite well, with plots and discussion of zero-point energy.)Goalpara College. “Particle in a 1-Dimensional Box.”
(Short PDF note emphasizing (E_n = \frac{n^2 h^2}{8mL^2}), quantization, and non-zero ground state energy.)PhysicsPages.com. “Finite Square Well – Bound States, Even Wave Functions.”
(Derives transcendental equations for bound states and contrasts oscillatory behavior inside the well with exponential decay outside.)