Textbooks

1. Griffiths, D. J., & Schroeter, D. F. (2018). Introduction to Quantum Mechanics (3rd ed.). Cambridge University Press.
   (Chapter 2: Full derivation using creation and annihilation operators)

2. Shankar, R. (2012). Principles of Quantum Mechanics (2nd ed.). Springer.
   (Chapter 6: Algebraic method emphasized; coherent states introduced)

3. Messiah, A. (1999). Quantum Mechanics (Vol. 1). Dover Publications.
   (Chapter IV: Analytic solution using Hermite polynomials (H_n(\xi)), recursion relations)

4. Sakurai, J. J., & Napolitano, J. (2020). Modern Quantum Mechanics (3rd ed.). Cambridge University Press.
   (Chapter 2: Operator algebra and number states)

5. OpenStax. (2016). University Physics Volume 3. OpenStax.
   https://openstax.org/details/books/university-physics-volume-3
   (Section 7.6: Introductory treatment, zero-point energy)

6. Ghatak, A. K., & Lokanathan, S. (2004). Quantum Mechanics: Theory and Applications (5th ed.). Macmillan Publishers India Limited.
   (Chapter 8: One dimensional barrier transmission problems)

Online Resources

Freely accessible derivations, simulations, and lecture materials.

1. Wikipedia contributors. (2026). Quantum harmonic oscillator.
   https://en.wikipedia.org/wiki/Quantum_harmonic_oscillator
   (Energy levels, ladder operators, 3D extensions)

2. Physics LibreTexts. (2025). 7.6: The Quantum Harmonic Oscillator.
   https://phys.libretexts.org/Bookshelves/University_Physics/University_Physics_(OpenStax)/.../7.6:_The_Quantum_Harmonic_Oscillator
   (Comparison of quantum and classical SHO)

3. Zwiebach, B. (2013). Quantum Physics I (MIT OpenCourseWare 8.04), Lecture 8: Quantum Harmonic Oscillator.
   https://ocw.mit.edu/courses/8-04-quantum-physics-i-spring-2013/resources/mit8_04s13_lec08/
   (PDF notes on time-dependent states)

4. Grünberg, P. (Ongoing). Linear Harmonic Oscillator. UIUC Physics Notes.
   https://www.ks.uiuc.edu/Services/Class/PHYS480/qm_PDF/chp4.pdf
   (Schrödinger equation and stationary states)