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(undergraduate course)
Topics: Wave-particle duality. Uncertainty principle. Solutions to Schrödinger’s Equation in One Dimension: Transmission and Reflection at a Barrier; Tunneling; Potential Wells; Harmonic Oscillator; Free Particle. Formalism: Hilbert Space, Observables, Hermitian Operators. Schrödinger’s Equation in Three Dimensions: Hydrogen Atom. Angular Momentum and Spin.
Book: Introduction to Quantum Mechanics, by David J. Griffiths
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YOUTUBE VIDEOS OF LECTURES:
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CHAPTER 1
*) The Schrödinger equation [18:28 min]
Sec.1.1 of Griffiths’ Quantum Mechanics book 3rd ed.
https://youtu.be/Slhiyfpktiw
*) The Statistical interpretation [21:54 min]
Sec.1.2 of Griffiths’ Quantum Mechanics book 3rd ed.
https://youtu.be/xAVbF6iVaWA
*) Probability (Discrete Variables) [31:15 min]
First part of Sec.1.3 of Griffiths’ Quantum Mechanics book 3rd ed.
https://youtu.be/LBa-nyRj0PM
*) Probability (Continuous Variables) [6:42 min]
Second part of Sec.1.3 of Griffiths’ Quantum Mechanics book 3rd ed.
https://youtu.be/TI9Lh_GEllI
*) Normalization [21:42]
Sec.1.4 of Griffiths’ Quantum Mechanics book 3rd ed. Physical wave functions are square integrable, they are normalizable. If the wave function is normalized t t=0, Schrödinger equation ensures its normalization at any other time.
https://youtu.be/42-tyjj2gFw
*) Momentum [22:11 min]
Sec.1.5 of Griffiths’ Quantum Mechanics book 3rd ed.
Expectation value of position, momentum, and other quantities.
https://youtu.be/F5ihErsPu2M
*) Uncertainty Principle [6:14 min]
Sec.1.6 of Griffiths’ Quantum Mechanics book 3rd ed.
A qualitative notion of the uncertainty principle involving x and p.
https://youtu.be/0FnND5RVPzg
CHAPTER 2
*) Time-independent Schrödinger equation [10:19 min]
Sec.2.1 First Part, from Eq. (2.1) to Eq.(2.6)
https://youtu.be/nXgsQCg_a7s
*) Stationary States [19:59 min]
Second part of Sec.2.1 of Griffiths’ Quantum Mechanics book 3rd ed. This video starts with Eq.(2.7) and ends with Eq.(2.15)
https://youtu.be/JOJgFfYyVsM
*) Wave function at time t [10:44 min]
This is the last part of Sec.2.1 of Griffiths’ Quantum Mechanics book 3rd ed. It starts with Eq.(2.16) and ends with Eq.(2.21)
https://youtu.be/6Jx6PvebYeY
*) Probability density (Example 2.1) [10:11 min]
https://youtu.be/ag6JsIr2XEw
*) Infinite Square Well [30.24 min]
Sec.2.2 of Griffiths’ Quantum Mechanics book. This video starts with eq.(2.22) and ends with eq.(2.31). We find the energies E_n and the corresponding states psi_n(x).
https://youtu.be/K6PJTRWgC54
*) Properties of the functions of the infinite square well [27:54 min]
This is a continuation of the discussion about the infinite square well in Griffiths’ Quantum Mechanics book 3rd ed. It starts with Eq.(2.32) and ends with Eq.(2.39).
https://youtu.be/FjY2E0_XuOo
CHAPTER 3
*) Hilbert space [29:46 min]
Sec.3.1
https://youtu.be/xcGDp6lk60o
CHAPTER 3 & 4
*) Example 3.8 and beginning of Chapter 4
https://youtu.be/b7j9a8YlhWM
*) Radial Equation for the Hydrogen Atom
Summary from Eq.4.35 to Eq.4.77
https://youtu.be/ItLbJjLeZdE
*) Hydrogen Atom
Lecture about the Hydrogen atom following Griffiths 3rd edition Chapter 4. Sec.4.2 up to Eq.(4.80)
https://youtu.be/t_PBK0nCDIY
*) Hydrogen atom and Angular Momentum
End of the discussion about Radial Wave Function and beginning of Sec.4.3 on Angular Momentum of Griffiths book 3rd edition.
https://youtu.be/JKNBHXzm9XE
*) Angular Momentum and Spin
Sec.4.3 on Angular Momentum of Griffiths’ book 3rd edition and it also has the beginning of Sec.4.4 on Spin
https://youtu.be/vuKShj6eSHs
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YOUTUBE VIDEOS OF SOLUTIONS:
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*) Prob. 1.3
https://youtu.be/ugOBTDnWuws
*) Gaussian integral
https://youtu.be/8o2bYQVE6BE
*) Prob. 1.4
https://youtu.be/yOyMVzVQVMk
*) Prob. 1.7
https://youtu.be/rSlP0jkqzCg
*) Prob. 1.9
https://youtu.be/K5sNMhdoyyc
*) Prob. 2.32
https://youtu.be/_FjwvuinlsQ
*) Prob. 3.5
https://youtu.be/45z8OuZ1uoc
*) Prob. 3.13
https://youtu.be/2LpSgYRFYak
*) Prob. 4.22
https://youtu.be/Z7WA2OPWaHE
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LECTURE NOTES:
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Lecture 01 (Chapter 1: probability, expectation value, Ehrenfest theorem, uncertainty principle)
Lecture 02 (Chapter 2, Sec.2.1: time-independent Schrödinger equation, stationary states)
Lecture 03a (Chapter 2, Sec.2.2: infinite square well)
Lecture 03b (Chapter 2, Sec.2.3.2: harmonic oscillator – analytic method)
Lecture 04 (Chapter 2, Sec. 2.3.1: harmonic oscillator – algebraic method)
Lecture 05 (Chapter 2, Sec. 2.4: free particle)
Lecture 06 (Chapter 2, Sec. 2.5: delta function)
Lecture 07 (Chapter 2, Sec. 2.6: finite square well)
Lecture 08 (Chapter 3: Formalism, Hilbert space, observables)
Lecture 09 (Chapter 3: Eigenvalues, eigenfunctions, generalized uncertainty principle)
Lecture 10 (Chapter 3: Dirac notation, position vs momentum representation)
Lecture 11 (Chapter 4: Quantum mechanics in 3D, spherical coordinates, radial and angular equations)
Lecture 12 (Chapter 4, Sec.4.3.1: Angular momentum)
Lecture 13 (Chapter 4, Sec.4.3.2: Angular momentum eigenfuctions)
Lecture 14 (Chapter 4, Sec.4.2: Hydrogen atom)
Lecture 15 (Chapter 4: Spin)
Lecture 16 (Chapter 4: Stern-Gerlach experiment)