Combine the two formulas for momentum.
|p = mv =||h||⇒||λ =||h|
This was basically Louis de Broglie's doctoral thesis of 1924.
Davisson-Germer experiment. A person entering a room with more than one entrance will always enter through one of them, not all of them at the same time. An electron, on the other hand, can and does enter enter a room through all doors simultaneously.
Kapitza-Dirac Effect: diffraction of a particle beam by a standing wave of light. Proposed in 1933. Observed by Herman Batelaan at the University of Nebraska in 2001.
Erwin Schrödinger (1887-1961) Austria, Abhandlungen zur Wellenmechanik. Wave equation for matter reminiscent of Maxwell's equations for electromagnetic waves. The story I heard is that Schrödinger went to Switzerland with two goals: to keep his mistress happy and to derive a wave equation for matter. How successful he was with the former is open to speculation.
full, time-dependent form
|iℏ||∂||Ψ(r, t) = −||ℏ2||∇2Ψ(r, t) + V(r)Ψ(r, t)|
can be separated into two halves
Ψ(r, t) = ψ(r)φ(t)
spatial, time-independent half
|Eψ(r) = −||ℏ2||∇2ψ(r) + V(r)ψ(r)|
φ(t) = e−iEt/ℏ
Quote to get things started.
Two seemingly incompatible conceptions can each represent an aspect of the truth … They may serve in turn to represent the facts without ever entering into direct conflict. (Louis de Broglie)
The defining feature of the microscopic world is the wave-particle duality. Whenever we observe elementary entities (like electrons or photons) they appear as a localized events. A single photon can be observed as a tiny dot on a photographic plate. A single electron can be observed as a tiny flash on a television screen. This locality (existing at a particular place) and temporality (occurring at a specific time) is what it means for a thing to exist as a particle. It interacts with its environment in a specific place at a specific time.
In contrast, when we are not observing these entities interacting with their environment, they behave in a wavelike manner — extended in space, diffracting around obstacles and through openings, interfering with other elementary entities of the same type (that is, electrons interfere with electrons, and photons with photons). The nature of the waves associated with elementary entities are probability waves — unitless numbers, numerical ratios. They tell you the probability of finding a particular particle at a particular place and time and nothing else. They do not measure the value of any physical quantity. The waves themselves carry no mass, no charge, no energy, no momentum, no angular momentum, no information of any sort other than the likelihood of existence. In essence, they carry information only. Nothing else.
The conflict between these two aspects of microscopic reality results in the Uncertainty Principle
|Δpx Δx ≥||ℏ|
Momentum and position are measured in the same direction.
|Δpx Δx ≥||ℏ||Δpy Δy ≥||ℏ||Δpz Δz ≥||ℏ|
Momentum–position becomes energy–time.
|ΔE Δt ≥||ℏ|
Formally, a function and its Fourier transform cannot both be compactly supported.
Quantum mechanics is like a student who always gets the correct answer to the first question in an exam, but never the second.
Werner Karl Heisenberg (1901-1976) Germany
Gott würfelt nicht.
I, at any rate, am convinced that He [God] is not playing at dice. Albert Einstein, letter (1926)
I cannot believe that God plays dice with the cosmos. Albert Einstein, Observer, 'Sayings of the Week', 5 Apr. 1953, but used earlier in letter to Max Born, 4 Dec. 1926
I am convinced that He (God) does not play dice. Albert Einstein
Not only does God play dice with the Universe - he sometimes casts them where they can't be seen. Stephen Hawking
It is often stated that of all the theories proposed in this century, the silliest is quantum theory. In fact, some say that the only thing that quantum theory has going for it is that it is unquestionably correct. Michio Kaku Hyperspace, Oxford University Press, 1995, p 263
Carroll, Lewis "Alice laughed: "There's no use trying," she said; "one can't believe impossible things." "I daresay you haven't had much practice," said the Queen. "When I was younger, I always did it for half an hour a day. Why, sometimes I've believed as many as six impossible things before breakfast." Alice in Wonderland.
What I am going to tell you about is what we teach our physics students in the third or fourth year of graduate school … It is my task to convince you not to turn away because you don't understand it. You see my physics students don't understand it … That is because I don't understand it. Nobody does.
A good simple application. Electrons have very little mass and therefore occupy a lot of volume. Protons are much more massive and occupy very little volume.
Absolute zero does not imply absolute rest. Zero point energy.
Casimir Effect — Hendrik Brugt Gerhard Casimir
In 1948, he published a famous paper with Dik Polder on the influence of retardation on the London- van der Waals forces. What is now known as the Casimir force has been convincingly demonstrated only recently. In 1996, Steve Lamoreaux at Los Alamos National Laboratories measured the force and found it to be in agreement with the Casimir- Polder theory.
F = π2ℏc A 240d4
I have taken Casimir's formulas, which are in Puthoff's papers, and calculated that two highly polished metal plates 200 kilometers by 200 kilometers on a side separated by one micron (a millionth of a meter) have enough potential energy to light a 100 Watt light bulb for a second. If we were to stumble upon 30 million or so of these structures out in space, we could hook them up to our light bulb and keep it lit for a year.
Tunneling is the only process by fusion could take place within the sun. The temperature is not sufficient for the hydrogen ions within the plasma that makes up the core of the sun to overcome the electrostatic repulsion between them. Instead, due to inherent uncertainty there is a certain probability that some of these ions will tunnel trough the Coulomb barrier. Once this reaction takes place, there is sufficient energy available for other reactions to take place such that the original hydrogens can fuse and decay until they become a nucleus of helium.
electron microscope related devices
More scalawags have hidden in the mires of quantum mechanics than legitimate science.