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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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| 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. |
| Midterm: |
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 - Mon. Oct. 20 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. |
| 20250924: | Pdf of notes/YouTube video |
| 20250922: | Pdf of notes/YouTube video |
| 20250917: | Pdf of notes/YouTube video |
| 20250915: | Pdf of notes/YouTube video |
| 20250910: | Pdf of notes/YouTube video |
| 20250908: | Pdf of notes/YouTube video |
| 20250903: | Pdf of notes/YouTube video |
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