Quantum Mechanics of a Particle in a Potential Well

Textbooks

  1. 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.)

  2. 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.)

  3. 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.)

  4. 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.)

  5. 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.)

  6. 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.)

  7. 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.

  8. 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

  1. 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.)

  2. Physics LibreTexts. “The Infinite Potential Well.” In General Physics (UCD Physics 7C).
    (Discusses boundary conditions, standing wave solutions, and quantized energies.)

  3. 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}).)

  4. Wikipedia. “Potential Well.” The Free Encyclopedia.
    (General concept of potential wells in classical and quantum contexts.)

  5. Wikipedia. “Quantum Well.” The Free Encyclopedia.
    (Applies the particle-in-a-box model to semiconductor quantum wells, including boundary conditions and energy levels.)

  6. 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

  1. 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.)

  2. 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.)

  3. 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.)