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Jake Bobowski ~Home~
PHYS 304 |
SCI 266 jake.bobowski@ubc.ca
Introduction to Qunatum Mechanics
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September / October / November / December / Top / Bottom
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| Nov. 24 - Assignment #6: |
Angular momentum and spin: Assignment #6 Recommended problems. This assignment won't be collected or graded. |
| Nov. 21 - Associated Legendre functions: |
Optional supplemental notes that work through the details of solving the theta-part of hydrogen's wavefunction. The notes start with:
- the ordinary differential equation derived in class |
| Nov. 6 - Assignment #5: |
The hydrogen atom: Assignment #5 Due Wednesday, Nov. 26 @ 14:00 |
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September / October / November / December / Top / Bottom
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| Oct. 30 - Assignment #4: |
Hermitian conjugate, commutators, uncertainty principle: Assignment #4 Due Monday, Nov. 17 @ 14:00 |
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Oct. 29: Reading Assignment |
Read and study chater 4 of Griffiths. |
| Oct. 24 - Midterm solns: | Here are the midterm solutions. |
| Oct. 17 - Midterm: |
Reminder: The PHYS 304 midterm has been moved to: Wednesday, Oct. 22 during the regular lecture time and in the usual lecture room. The midterm will cover chapters 1 and 2 from Griffiths. |
| Oct. 15 - Formula Sheet & Calculator: |
You can prepare your own formula sheet for the final exam. You can bring one 8.5" x 11" letter-sized piece of paper to the exam with anything written or printed on it. You can use both sides of the paper. You can bring any calculator that cannot go online or wirelessly communicate with another device. Graphing calculators are fine. |
| Oct. 15 - Final Exam: |
The PHYS 304 final exam has been scheduled for:
Thursday, Dec. 11 |
| Oct. 9 - Assignment #3: |
Free particle and scattering states: Assignment #3 Due Monday, Oct. 27 @ 14:00 Although this assignment is not due until after the midterm, you should try these chapter 2 problems before the midterm. |
| Oct. 9 - Quantum well analog: | Optional supplemental notes that explore a classical transmission-line-based analog of the finite square well scattering states and the bound states (i.e. stationary states) of an infinite square well. These optional notes would be most useful for those that have seen transmission lines in PHYS 331. |
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Oct. 7: Reading Assignment |
Read and study chater 3 of Griffiths. |
| Oct. 7 - Midterm: |
You may also bring with you a single letter-sized piece of paper (8.5 x 11) with anything written on it (both sides). You may bring any calculator that cannot go online. Graphing calculators are fine. |
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Oct. 7 - Midterm: updated Oct. 17 |
Reminder: The PHYS 304 midterm will be on Wednesday, Oct. 22 during the regular lecture time and in the usual lecture room. The midterm will cover chapters 1 and 2 from Griffiths. |
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September / October / November / December / Top / Bottom
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| Sept. 28 - Assignment #2: |
Infinite Square Well and Harmonic Oscillator: Assignment #2 Due Wednesday, Oct. 8 @ 14:00 |
| Sept. 25 - Jupyter link: |
Python code to visualize wavepackets assembled from the stationary states of the infinite square well: Open Jupyter link. |
| Sept. 24 - History: |
The solutions to Schrodinger's equation that we're studying for various potentials V(x) were worked out hundreds of years ago long before the birth of quantum mechanics. Here's a brief sketch of the timeline.
Foundations of Analysis → Quantum Mechanics (Quick Timeline)Foundations of Analysis & ODEs
Newton & Leibniz
(1660s–70s)
Invention of calculus. → Made it possible to even write down differential equations of motion.
Euler
(1707–1783)
Systematic study of infinite series and special functions. → Early work on series solutions, gamma function, and exponential/trig expansions. Classical Mathematical Physics
Lagrange & Laplace
(18th century)
Celestial mechanics; ODE/PDE techniques. → Stimulated development of polynomial solutions for orbital problems.
Fourier
(1768–1830)
Fourier series (1807). → Decomposition of functions into modes = prototype of spectral decomposition in QM.
Legendre
(1752–1833)
Legendre polynomials (1782). → Show up in angular solutions of the hydrogen atom.
Bessel
(1784–1846)
Bessel functions (1817, optics & astronomy). → Later appear in radial wave equations, scattering theory. 19th Century: Orthogonal Functions & Sturm–Liouville
Sturm & Liouville
(1830s)
Theory of eigenfunction expansions with weight functions. → Direct ancestor of QM’s “complete orthonormal basis.”
Hermite
(1822–1901)
Hermite polynomials (probability, optics). → Exactly the functions in the harmonic oscillator.
Laguerre
(1834–1886)
Laguerre polynomials. → Appear in the hydrogen radial wavefunction. Turn of the 20th Century
Hilbert, Riesz, et al.
(1900–1920)
Functional analysis, Hilbert spaces. → Gave rigorous mathematical footing to infinite-dimensional expansions. Quantum Mechanics (1920s onward)
Schrödinger, Heisenberg, Dirac…
Quantum mechanics born. → All those 18th/19th-century “special functions” became the natural solutions of the fundamental wave equations. |
| Sept. 21 - Harmonic Oscillator: |
Optional supplemental notes that show how we can analytically deduce the coherent oscillation of the probability denisty of a particular initial state of the quantum harmonic oscillator. Fair warning: The calculation is doable, but somewhat involved. |
| Sept. 21 - Jupyter link: |
Python code to visualize the time evolution of the probabilty density for a quantum harmonic oscillator coherent state: Open Jupyter link. |
| Sept. 17 - Jupyter link: |
Python code to visualize the time evolution of the probabilty density for a particle in an inifinite square well using the initial state adopted for the example discussed in lecutre: Open Jupyter link. |
| Sept. 15 - Assignment #1: |
Probability and Expectation Values: Assignment #1 Due Wednesday, Sept. 24 @ 14:00 |
| Reading Assignment | Read and study chapter 2 of Griffiths. |
| Reading Assignment | Read and study chapter 1 of Griffiths. |
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Midterm: updated Oct. 17 |
The will be one midterm in PHYS 304. It will be written during regular class time and in the usual class room. The midterm is scheduled for: Midterm - Wed. Oct. 22 There will not be a make-up midterm. |
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Piazza: |
A Piazza page has been created for PHYS 304. To enroll, use the link found in the PHYS 304 Canvas page. |
| Course Syllabus (.pdf): | PHYS 304 Syllabus |
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Lecture Notes |
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| Playlist: | PHYS 304 YouTube playlist. |
| 20251203: | Pdf of notes/YouTube video |
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| 20251020: |
Pdf of notes Ran into some technical issues with logging into Zoom. There is no recording of this class. I beleive that the issue has been now been resolved. |
| 20251015: | Pdf of notes/YouTube video |
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