Analog quantum computer Updated +Created
Video 1.
TensorFlow quantum by Masoud Mohseni (2020)
Source. At the timestamp, Masoud gives a thought experiment example of the perhaps simplest to understand analog quantum computer: chained double-slit experiments with carefully calculated distances between slits. Calulating the final propability distribution of that grows exponentially.
de Broglie relations Updated +Created
Relates particle momentum and its wavelength, or equivalently, energy and frequency.
The wavelength relation is:
but since:
the wavelength relation implies:
Particle wavelength can be for example measured very directly on a double-slit experiment.
So if we take for example electrons of different speeds, we should be able to see the diffraction pattern change accordingly.
Interference pattern Updated +Created
What you see along a line or plane in a wave interference.
Notably used for the pattern of the double-slit experiment.
Path integral formulation Updated +Created
This one might actually be understandable! It is what Richard Feynman starts to explain at: Richard Feynman Quantum Electrodynamics Lecture at University of Auckland (1979).
The difficulty is then proving that the total probability remains at 1, and maybe causality is hard too.
The path integral formulation can be seen as a generalization of the double-slit experiment to infinitely many slits.
Feynman first stared working it out for non-relativistic quantum mechanics, with the relativistic goal in mind, and only later on he attained the relativistic goal.
TODO why intuitively did he take that approach? Likely is makes it easier to add special relativity.
This approach more directly suggests the idea that quantum particles take all possible paths.
Photon Updated +Created
Initially light was though of as a wave because it experienced interference as shown by experiments such as:
But then, some key experiments also start suggesting that light is made up of discrete packets:and in the understanding of the 2020 Standard Model the photon is one of the elementary particles.
This duality is fully described mathematically by quantum electrodynamics, where the photon is modelled as a quantized excitation of the photon field.
Planck constant Updated +Created
Proportionality factor in the Planck-Einstein relation between light energy and frequency.
And analogously for matter, appears in the de Broglie relations relating momentum and frequency. Also appears in the Schrödinger equation, basically as a consequence/cause of the de Broglie relations most likely.
Intuitively, the Planck constant determines at what length scale do quantum effects start to show up for a given energy scale. It is because the Plank constant is very small that we don't perceive quantum effects on everyday energy/length/time scales. On the , quantum mechanics disappears entirely.
A very direct way of thinking about it is to think about what would happen in a double-slit experiment. TODO think more clearly what happens there.
Defined exactly in the 2019 redefinition of the SI base units to:
Schrödinger equation Updated +Created
Experiments explained:
Experiments not explained: those that the Dirac equation explains like:
To get some intuition on the equation on the consequences of the equation, have a look at:
The easiest to understand case of the equation which you must have in mind initially that of the Schrödinger equation for a free one dimensional particle.
Then, with that in mind, the general form of the Schrödinger equation is:
Equation 1.
Schrodinger equation
.
where:
  • is the reduced Planck constant
  • is the wave function
  • is the time
  • is a linear operator called the Hamiltonian. It takes as input a function , and returns another function. This plays a role analogous to the Hamiltonian in classical mechanics: determining it determines what the physical system looks like, and how the system evolves in time, because we can just plug it into the equation and solve it. It basically encodes the total energy and forces of the system.
The argument of could be anything, e.g.:
Note however that there is always a single magical time variable. This is needed in particular because there is a time partial derivative in the equation, so there must be a corresponding time variable in the function. This makes the equation explicitly non-relativistic.
The general Schrödinger equation can be broken up into a trivial time-dependent and a time-independent Schrödinger equation by separation of variables. So in practice, all we need to solve is the slightly simpler time-independent Schrödinger equation, and the full equation comes out as a result.
Single particle double slit experiment Updated +Created
This experiment seems to be really hard to do, and so there aren't many super clear demonstration videos with full experimental setup description out there unfortunately.
For single-photon non-double-slit experiments see: single photon production and detection experiments. Those are basically a pre-requisite to this.
photon experiments:
Non-elementary particle:
  • 2019-10-08: 25,000 Daltons
  • interactive.quantumnano.at/letsgo/ awesome interactive demo that allows you to control many parameters on a lab. Written in Flash unfortunately, in 2015... what a lack of future proofing!
Video 1.
Single Photon Interference by Veritasium (2013)
Source. Claims to do exactly what we want, but does not describe the setup precisely well enough. Notably, does not justify how he knows that single photons are being produced.
SQUID device Updated +Created
Can be used as a very precise magnetometer.
There are high temperature yttrium barium copper oxide ones that work on liquid nitrogen.
Video 1.
Superconducting Quantum Interference Device by Felipe Contipelli (2019)
Source. Good intuiotionistic video. Some points deserved a bit more detail.
Video 2.
Mishmash of SQUID interviews and talks by Bartek Glowaki
. Source.
The videos come from: www.ascg.msm.cam.ac.uk/lectures/. Vintage.
Mentions that the SQUID device is analogous to a double-slit experiment.
One of the segments is by John Clarke.
Video 3.
Superconducting Quantum Interference Devices by UNSW Physics (2020)
Source.
An experimental lab video for COVID-19 lockdown. Thanks, COVID-19. Presented by a cute and awkward Adam Stewart.
Uses a SQUID device and control system made by STAR Cryoelectronics. We can see Mr. SQUID EB-03 written on the probe and control box, that is their educational product.
As mentioned on the Mr. SQUID specs, it is a high-temperature superconductor, so liquid nitrogen is used.
He then measures the I-V curve on an Agilent Technologies oscilloscope.
Unfortunately, the video doesn't explain very well what is happening behind the scenes, e.g. with a circuit diagram. That is the curse of university laboratory videos: some of them assume that students will have material from other internal sources.
Video 4.
The Ubiquitous SQUID by John Clarke (2018)
Source.