Quantum Mechanics

Instructor Information

• Instructor: Dr. William Thorne (Professor of Physics)
• Email: wthorne@university.alkimi.ai
• Office: Meridian Science Center 410
• Office Hours:
  • Monday & Thursday: 10:00–11:30 a.m. (In person, Meridian Science Center 410)
  • Wednesday: 3:00–4:00 p.m. (Virtual via Zoom; link posted in Canvas)
  • Also available by appointment.

Course Description

Wave functions and operators, the Schrödinger equation in one and three dimensions, the harmonic oscillator, the hydrogen atom, angular momentum and spin, identical particles, and perturbation theory. PHYS 410 is an advanced, mathematically formal study of non-relativistic quantum mechanics for senior physics majors. Formulating the theory in Hilbert space using Dirac bra-ket notation, we investigate state vectors, Hermitian operators, observables, and generalized uncertainty relations. The course thoroughly develops the quantum harmonic oscillator via ladder operators, central force problems, orbital and spin angular momentum addition, systems of identical particles, and time-independent perturbation theory.

Prerequisites

PHYS 221, MATH 250, and MATH 340.

Measurable Student Learning Outcomes

Upon successful completion of PHYS 410, students will be able to:

1. Apply Hilbert Space Formalism and Dirac Notation: Operate with state vectors, projection operators, Hermitian observables, and unitary transformations in finite and infinite-dimensional Hilbert spaces.
2. Solve the Quantum Harmonic Oscillator Analytically and Algebraically: Derive energy eigenvalues and eigenfunctions of the harmonic oscillator using both differential equations and raising/lowering operator techniques.
3. Analyze Angular Momentum and Spin Coupling: Calculate commutation relations for orbital and spin angular momentum operators, determine eigenvalue spectra, and compute Clebsch-Gordan coefficients.
4. Solve Three-Dimensional Central Potentials: Solve the radial Schrödinger equation for spherical potentials, derive the hydrogen atom spectrum, and construct radial wavefunctions and spherical harmonics.
5. Evaluate Many-Particle Systems and Exchange Symmetry: Construct symmetric and antisymmetric states for systems of identical bosons and fermions, analyzing exchange forces and the helium atom ground state.
6. Implement Time-Independent Perturbation Theory: Calculate first- and second-order energy shifts and wave function corrections for non-degenerate and degenerate systems, applying techniques to fine structure and Zeeman effects.

Required Course Materials & Approximate Costs

1. Griffiths, David J., and Darrell F. Schroeter. Introduction to Quantum Mechanics. 3rd ed., Cambridge University Press, 2018. Approx. $60 for digital; approx. $85 for print purchase.
2. Total estimated cost: $60 to $85.

Generative AI Policy (AI Level 2: AI Permitted with Disclosure for Specified Tasks)

In accordance with Alkimi University Academic Policies (Student Handbook §5.8), PHYS 410 operates under AI Level 2.

• What is permitted: You may use AI tools to check matrix diagonalizations, verify commutators between operators, explore Dirac bra-ket notation manipulations, and generate practice problems for perturbation theory.
• What is prohibited: You may not submit AI-generated derivations or proofs for weekly homework problem sets, copy AI solutions for take-home or in-class exams, or consult any generative AI during examinations.
• Disclosure: Provide a written statement at the end of every submitted problem set indicating which AI tools were consulted and explaining your independent verification of all quantum calculations, or confirm no AI tools were used.

Grading Components and Weights

• Midterm Exam 1: 20% (In class, Friday, September 25)
• Midterm Exam 2: 20% (In class, Friday, October 30)
• Weekly Advanced Problem Sets: 25% (Due Fridays at 11:59 p.m. in Canvas (weeks 2–13; lowest dropped))
• Quantum Mechanics Term Paper: 10% (Due Friday, November 20 at 11:59 p.m.)
• Final Comprehensive Examination: 25% (Wednesday, December 16, 2026, 3:30–5:30 p.m.)

Grading Scale (Alkimi University Standard)

• A: 93–100% | A-: 90–92%
• B+: 87–89% | B: 83–86% | B-: 80–82%
• C+: 77–79% | C: 73–76% | C-: 70–72%
• D+: 67–69% | D: 60–66% | F: Below 60%
• Extra credit: No extra credit assignments are offered in PHYS 410.

Course Schedule (Fall 2026)

Course Policies

Attendance Policy

Attendance at every seminar meeting is mandatory. Advanced quantum mechanics requires collaborative chalkboard derivations, rigorous conceptual dialogue, and active questioning. If you must miss a class due to illness or academic conference travel, notify Dr. Thorne via email in advance. More than three unexcused absences will result in a penalty to your final course grade. Students who miss the first two class meetings without notifying the instructor may be dropped. Students may miss class for religious observance without penalty if they notify the instructor in writing within the first two weeks of the semester (by Wednesday, September 9, 2026). Absences for university-sponsored activities (athletics, performances, conferences) are excused with a letter from the sponsoring office at least one week in advance.

Late Work Policy

Problem sets submitted within 24 hours of the Friday deadline receive a 20% penalty. Because solution packets are distributed immediately thereafter, no problem sets will be accepted after 24 hours. The single lowest weekly problem set score will be dropped.

Final Exam Policy

The final examination (Wednesday, December 16, 2026, 3:30–5:30 p.m.) is scheduled by the University Registrar and can't be moved without the Dean's written approval (Faculty Handbook §5.5). A student with three or more final exams on the same calendar day may reschedule one of them. Requests go to the instructor of the middle exam by the last day of classes. For this term, send the request by Wednesday, December 9, 2026 (Student Handbook §6.4).