A relativistic version of the Schrödinger equation.
Correctly describes spin 0 particles.
The most memorable version of the equation can be written as shown at Section "Klein-Gordon equation in Einstein notation" with Einstein notation and Planck units:
Has some issues which are solved by the Dirac equation:
- it has a second time derivative of the wave function. Therefore, to solve it we must specify not only the initial value of the wave equation, but also the derivative of the wave equation,As mentioned at Advanced quantum mechanics by Freeman Dyson (1951) and further clarified at: physics.stackexchange.com/questions/340023/cant-the-negative-probabilities-of-klein-gordon-equation-be-avoided, this would lead to negative probabilities.
- the modulus of the wave function is not constant and therefore not always one, and therefore cannot be interpreted as a probability density anymore
- since we are working with the square of the energy, we have both positive and negative value solutions. This is also a features of the Dirac equation however.
Bibliography:
- Video "Quantum Mechanics 12a - Dirac Equation I by ViaScience (2015)" at youtu.be/OCuaBmAzqek?t=600
- An Introduction to QED and QCD by Jeff Forshaw (1997) 1.2 "Relativistic Wave Equations" and 1.4 "The Klein Gordon Equation" gives some key ideas
- 2011 PHYS 485 lecture videos by Roger Moore from the University of Alberta at around 7:30
- www.youtube.com/watch?v=WqoIW85xwoU&list=PL54DF0652B30D99A4&index=65 "L2. The Klein-Gordon Equation" by doctorphys
- sites.ualberta.ca/~gingrich/courses/phys512/node21.html from Advanced quantum mechanics II by Douglas Gingrich (2004)
Discovered by Marie Curie, published July 1999.
Ciro Santilli often wonders to himself, how much of the natural sciences can one learn in a lifetime? Certainly, a very strong basis, with concrete experimental and physics, chemistry and biology should be attainable to all? How much Ciro manages to learning and teach in those areas is a kind of success metric of Ciro's life.
www-pnp.physics.ox.ac.uk/~barra/teaching.shtml As of 2023, contains some good 2015 materials: web.archive.org/web/20220525094139/http://www-pnp.physics.ox.ac.uk/~barra/teaching.shtml It was called "Subatomic physics" back then.
2015 professor: Alan J. Barr.
Possible 2022 professor: Guy Wilkinson (unconfirmed): www.chch.ox.ac.uk/staff/professor-guy-wilkinson
users.ox.ac.uk/~corp0014/B6-lectures.html gives a syllabus:
- Heat capacity in solids, localised harmonic oscillator models (Dulong-Petit law and Einstein model)
- Heat capacity in solids, a model of sound waves (Debye model)
- A gas of classical charged particles (Drude theory)
- A gas of charged fermions (Sommerfeld theory)
- Bonding
- Microscopic theory of vibrations: the 1D monatomic harmonic chain. Mike Glazer's Chainplot program.
- Microscopic theory of vibrations: the 1D diatomic harmonic chain
- Microscopic theory of electrons in solids: the 1D tight-binding chain
- Geometry of solids: crystal structure in real space. VESTA, 3D visualization program for structural models; an example crystal structure database.
- Geometry of solids: real space and reciprocal space. Reciprocal Space teaching and learning package.
- Reciprocal space and scattering. A fun way to discover the world of crystals and their symmetries through diffraction.
- Scattering experiments II
- Scattering experiments III
- Waves in reciprocal space
- Nearly-free electron model
- Band structure and optical properties
- Dynamics of electrons in bands
- Semiconductor devices. Intel's "A History of Innovation"; Moore's Law; From Sand to Circuits.
- Magnetic properties of atoms
- Collective magnetism. A micromagnetic simulation tool, The Object Oriented MicroMagnetic Framework (OOMMF); OOMMF movies of magnetic domains and domain reversal.
- Mean field theory
Problem set dated 2015: users.ox.ac.uk/~corp0014/B6-materials/B6_Problems.pdf Marked by: A. Ardavan and T. Hesjedal. Some more stuff under: users.ox.ac.uk/~corp0014/B6-materials/
The book is the fully commercial The Oxford Solid State Basics.
The only isotope found on Earth because it occurs as part of the uranium 238 decay chain, i.e., it is not a primordial nuclide.
Interestingly it is a bit less stable than other isotopesL such as Polonium-208 (3 y) and Polonium-209 (124 y), but those aren't in any Earthly radioactive chain so they don't show up on Earth.
A really good option to store educational media such as images and video!
Shame that like the rest of Wikimedia, their interface is so clunky and lacking obvious features.
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