Penetration factor for slowly varying barriers – David Miller — Quantum Academy Video Library

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10 videos · 5 h 22 min

Lecture · Stanford
Barriers and boundary conditions – David Miller
David Miller Quantum Mechanics Courses · David A. B. Miller
Stanford's David Miller shows why ψ and dψ/dz must both be continuous, then sends a wave at an infinitely thick barrier: inside, ψ falls off as e^(−κz) instead of stopping dead, and the barrier still reflects 100% but with a phase shift that has no classical analogue. His worked example is section 1's own: an electron of 1 eV meeting a 2 eV barrier, giving an amplitude decay length 1/κ of about 0.2 nm and a probability decay length of about 0.1 nm.
- Ch 12
Lecture · Instituto de Física
Measuring the Tunneling Time, and Other Problems in Quantum Archaeology | COLÓQUIOS IFUSP
Instituto de Física USP · Aephraim Steinberg
A University of São Paulo physics colloquium by Aephraim Steinberg of Toronto, whose experiments section 7 describes: from "Background" (12:39) he covers the stationary-phase approach (14:15), defines a Larmor time (24:43), introduces the atoms (25:53) and walks through the tunnelling experiment (27:54). Advanced, but it shows how "time spent inside a barrier" can be measured at all.
- Ch 12
Lecture · MIT
Lecture 12: The Dirac Well and Scattering off the Finite Step
MIT OpenCourseWare · Allan Adams · 2013
The lecture from MIT 8.04 Quantum Physics I (Allan Adams, 2013) that goes with Chapter 12. The whole course is in the Lecture Hall.
- Ch 12
Lecture · Oxford
015 Tunnelling and Radioactive Decay
University of Oxford · James Binney · 2009–10
The lecture from University of Oxford Quantum Mechanics (James Binney, 2009–10) that goes with Chapter 12. The whole course is in the Lecture Hall.
- Ch 12
Course · MIT
Quantum Physics I
MIT OpenCourseWare · Allan Adams · 2013
Allan Adams' celebrated course starts from superposition and the experimental facts, builds the wavefunction, operators and the Schrödinger equation, then tours scattering, hydrogen, identical particles and band structure before closing on entanglement and Bell's theorem. Calculus and a little linear algebra are enough to keep up.
- Ch 01
- Ch 04
- and 14 more chapters
Course · MIT
Quantum Physics I
MIT OpenCourseWare · Barton Zwiebach · 2016
The same course rebuilt as 115 short segments of roughly ten to twenty minutes, each devoted to one idea, so you can watch exactly the concept a chapter needs. Barton Zwiebach is meticulous: every step on the board is justified.
- Ch 04
- Ch 06
- and 8 more chapters
Explainer · YouTube
What is Quantum Tunneling, Exactly?
Up and Atom
A friendly ten-minute tour that builds tunnelling from light: an evanescent wave leaks a short way past a surface that totally reflects light, and an electron's wavefunction fades into a barrier in the same way, leaving a small chance of finding it on the far side. As you watch, ask what would happen to that chance if the barrier were twice as thick.
- Ch 12
Lecture · YouTube
What is Quantum Tunnelling?
Physics Explained
A forty-minute deep dive that starts from the alpha-decay paradox Rutherford faced, matches the wavefunction and its slope at the barrier edges to reach an explicit tunnelling probability, then approximates the real Coulomb barrier to estimate half-lives. Watch it after Parts 2 and 3, with our transmission formulas and the worksheet's Gamow challenge beside you.
- Ch 12
Explainer · YouTube
The 2025 Nobel Prize in Physics (quantum tunnelling) - Sixty Symbols
Sixty Symbols
Physicists from the University of Nottingham unpack the 2025 Nobel Prize in Physics, awarded for macroscopic quantum tunnelling and energy quantisation in a superconducting circuit. Watch it after Part 6 to see how an entire circuit can tunnel.
- Ch 12
Explainer · YouTube
The Quantum Barrier Potential Part 2: Defining the Transmission and Reflection Coefficients
Professor Dave Explains
The full barrier calculation behind section 2's formula, worked step by step: reflection and transmission coefficients (from 2:54), the transmission factor T (5:33), hyperbolic sines and cosines (10:29) and an application (18:48). Once 2κL is large, the exact result shrinks to the lesson's T ≈ 16(E/V)(1 − E/V)e^(−2κL); plug in E = 1 eV, V = 2 eV and L = 0.5 nm and check that you get about 2.4%.
- Ch 12