Questions tagged [quantum-mechanics]
The branch of physics that relates to the behavior of objects, typically particles, on small scales. Probability is very important in quantum mechanics.
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Who first proposed the idea of "resolution of the identity"?
Who first proposed the idea of "resolution of the identity" as used in the functional calculus of self-adjoint operators? Was it von Neumann?
In Japanese, it translates as "resolution ...
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What technology was used to determine the shape of the blackbody spectrum at the 19th century?
The shape of the blackbody radiation spectrum was known in the 19th century from experimental measurements, and before the theoretical discovery of Planck's law.
At those times, how did people manage ...
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How did Stern or Gerlach, of Stern-Gerlach experiment, create individual silver atoms? How were they accelerated?
How, a century ago, could Stern and/or Gerlach KNOW that they had created single silver atoms?
How were they moved, or accelerated?
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Bohr-Kramers-Slater (BKS) theory and energy conservation only on statistically basis
I was reading Wikipedia article on Bohr-Kramers-Slater (BKS) theory, https://en.wikipedia.org/wiki/BKS_theory. I encountered two interesting points and need your help to understand the reasons behind ...
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Need quote from early 20th century about humanity probably never being able to control (manipulate, see?) a single quantum system
I remember having read a statement, I think by one of the founding fathers of quantum mechanics, that we will probably never be able to control (or manipulate or see or isolate...?) a single quantum ...
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On the origin of "sandwiches" in quantum mechanics
The term "sandwich" and the verb "to sandwich" appear pretty common but informally in quantum mechanics. Generally when describing some kind of inner product of the form:
$$\langle ...
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Why are pilot waves in quantum mechanics said to be Faraday waves?
De Broglie proposed a pilot wave in connection with quantum mechanics. He was more or less forced to abandon this wave in favor of the Copenhagen view. Bohm furthered his approach in the fifties but ...
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188 views
Why didn't the phase space formulation of Quantum Mechanics get the upper hand?
At university I learned quantum mechanics in or position or momentum variables. Later (in fact on this site), I learned about the phase space formulation in which both are used at the same time.
The ...
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What is the origin of the probability interpretation of quantum mechanics?
Born came up with his probability interpretation of quantum mechanics. But why did he think about such an interoretation? Why not thinking that a deterministic process has to lay at its foundation? ...
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206 views
Why did the Copenhagen interpretation of quantum mechanics got the upperhand?
The Copenhagen interpretation of quantum mechanics is nowadays the interpretation that prevails over other interpretations (or theories). Basically, it states that all processes in Nature are ...
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142 views
Origin of the recurrence relation for Clebsch-Gordan coefficients
The Clebsch-Gordan coefficients $C_{\pm }(J,M)$ arise in quantum mechanics in the problem of addition of angular momentum. They also arise in mathematics in the more theoretical (but related) problem ...
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A technical and historical introduction to quantum mechanics
I am curious to understand the history of QM. In particular, how did the physicists conclude that observables can be treated as operators, or the use of complex state spaces, or that Eigenvalues of ...
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Was Landau interested in the interpretations of quantum mechanics?
I am interested in Lev Landau. I was trying to find what was his approach to the interpretation of quantum mechanics, I am unable to find any particular source were this is discussed.
Was he an ...
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What are the definitive experiments/phenomena which motivate quantum mechanics?
The double slit experiment is usually given as the foremost example of a physical experiment that requires quantum mechanics to satisfactorily explain. However, every account i've seen of it (such as ...
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Dirac's non-neglibile disturbances argument and epistemic quantum mechanics
Here is Dirac's argument about one reason to motivate quantum mechanics:
"It is usually assumed that, by being careful, we may cut down the disturbance accompanying our observation to any desired ...
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107 views
Origins of the canonical commutation relation
I have recently been reading Gunter Ludwig's book wave mechanics to get a better understanding of quantum mechanics and in reading through the book I came across the relation
$$m\sum_s \{|q_{rs}|^2\...
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Background on the Stone-von Neumann theorem
I'm a mathematician.
I'm required to give a lecture on the Stone-von Neumann theorem. I already have all the mathematical details figured out, but I wish to make the lecture more interesting by giving ...
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Was Planck's Constant a huge leap conceptually? [duplicate]
It must have been observed, for example, that there was no element lighter than hydrogen or that there were not different-charged electrons (I believe the electron was discovered prior to Planck's ...
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Has someone ever proposed a "many worlds/histories" model where all possible boundary conditions are considered? [closed]
The Hawking-Hartle no boundary condition is a well known model that tries to explain how did the universe begin. The authors considered a "many worlds/histories" model considering a sum over ...
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Did Hugh David Politzer work independently for his contribution to asymptotic freedom?
The Nobel Prize was awarded to David Gross, Frank Wilczek and Hugh David Politzer. I believe David Gross worked with Frank Wilczek and was his thesis advisor.
On the other hand, I couldn't find much ...
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Original derivation of the Dyson equation
In what paper did Dyson derive the Dyson equation, as shown on Wikipedia?
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Heisenberg's last work on a non-linear generalization of quantum mechanics?
It is claimed here that toward the end of his life Werner Heisenberg worked on a non-linear broadening or generalization of quantum mechanics. What work was that? Was it published?
Is it listed in ...
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225 views
What is the source of a quotation by Niels Bohr?
The quote is:
When asked ... [about] an underlying quantum world, Bohr would answer,
'There is no quantum world. There is only an abstract quantum physical
description. It is wrong to think that the ...
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Did Rydberg ever learn of Bohr's quantum-mechanical explanation of his formula?
The Rydberg formula on the wavelengths of a spectral line in chemical elements was first stated empirically in 1888 by Johannes Rydberg. A theoretical explanation of the formula wouldn't arive until ...
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Understanding Bohr's response to a 1930 Einstein thought experiment that challenged the uncertainty principle
Structure of this post
I want to better understand how Bohr responded to Einstein's 1930 attempt to demonstrate that quantum mechanics was inherently contradictory under the Copenhagen interpretation....
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Quantum chromodynamics - an origin of the name
A theory of strong interaction is called quantum chromodynamics (QCD). Particles interacting strongly are supposed to have color charge, for example quarks appear in three "mutations" - red, green and ...
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How to get to Planck’s radiation law as Planck did it (warts and all)?
I would like to know how Planck went from an expression for the number of ways energy can be distributed in oscillators (denoted $W$) via the Boltzmann equation ($ S = k \ln W$) to the Planck ...
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Did the mathematician Garrett Birkhoff ever work with or mention Feynman's path integrals?
Did Garrett Birkhoff ever work with Feynman's path integral? Did he ever work in his Many-Histories interpretation? Or at least, did he mention it in any of his articles?
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Did Einstein or the scientific community know about quantum tunneling during the EPR debates?
It is my understanding that Einstein produced the EPR paper to necessarily elucidate the existence of physical properties that could not exist prior to measurement. That was his assumption which was ...
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Was Von Neumann and Birkhoff's original formulation of Quantum Logic related with projective geometry?
I was looking at how did von Neumann and Birkhoff formulate their Quantum Logic formalism back in 1936. To solve some questions, I contacted via email a philosopher who studied this topic.
I thought ...
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113 views
Did Weizsäcker's change his mind about time being a fundamental object?
I have some questions about von Weizsäcker's views in physics, which I find them generally interesting. One of them is that he thought that time was fundamental (he even thought that logic, which is ...
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The history of the equation $\boldsymbol {Et}-\boldsymbol {tE}=\frac{h}{2\pi i}$
Heisenberg already in 1927 quotes this equation as a "known equation".1
Then what is the origin of it? And what is its further history of it, ending in its death?
1 Über den anschaulichen Inhalt der ...
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Who introduced the "dagger"symbol as conjugate transpose in quantum mechanics?
The $\dagger$ symbol is often used in quantum mechanics,and also often in general mathematics to represent the conjugate transpose operation.For Hermitian matrices we can write $$A^\dagger=A$$Who ...
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What did Hans Bethe think of von Neumann's quantum logic?
Nobel laureate Hans Bethe was a friend of mathematician-physicist John von Neumann, and he once said:
"I have sometimes wondered whether a brain like von Neumann's does not indicate a species ...
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What is the original source for Einstein's description of entanglement as "Spooky Action at a Distance"?
Try as I may, I cannot find the original source where Einstein described entanglement as "Spooky Action at the Distance." The work "spooky" is not in the 1935 EPR paper, which was written in English ...
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105 views
How did Bohr guess the quantization rule?
We all know Bohr's quantization rule as $L = \frac{nh}{2\pi}$. How did Bohr derive this?
If it is a guess, what is the reason behind choosing $\frac{h}{2\pi}$ and not some other constant? Why did he ...
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579 views
What is the origin of the concept of reduced mass?
I am looking for the origin of the concept of reduced mass as used in vibrational spectroscopy e.g. vibration of a diatomic molecule. Most of the texts simply define reduced mass as the sum of the ...
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How was it determined that the photoelectric effect is independent of the intensity of light?
How as light intensity measured or determined around 1900? For example, when it was determined that the photoelectric effect was independent of the intensity of the light beam, but rather that it ...
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How did $SU(2)$ came into physics?
It is natural for physicists to consider the group $SO(3)$. Presumably, $SU(2)$ came into physics because of quantum mechanics. How did people realize that when studying rotation of a physical system, ...
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Why do many names of technical and scientific subjects end with "ics"?
The names of many technical and scientific subjects, like mathematics, physics, statistics, etc., etc., end with letters "ics". What is meant by this, if anything? Was there any logic behind it or is ...
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Do other branches of modern science have interpretations like Quantum Mechanics does?
As a layperson, when one learns about Quantum Mechanics, one also learns about the various interpretations of QM-- Many Worlds, Collapse, Pilot Wave theory, etc.
However, as far as I can tell (from ...
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What did Sommerfeld mean by Bohr's magic wand?
Background
From wikipedia:
"Bohr's correspondence principle demands that classical physics and quantum physics give the same answer when the systems become large.[5] A. Sommerfeld (1924) referred ...
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244 views
Where did Einstein propose interpreting the square of amplitude as probability density (Born's rule)?
In Max Born's Nobel lecture, he alludes to Einstein's proposed interpretation of EM wave amplitude (squared) as being the probability density of detecting a photon:
Again an idea of Einstein’s gave ...
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Did Werner Heisenberg ever agree or propose the existence of some kind of multiverse?
I was watching a video (https://www.youtube.com/watch?v=muJYTeQlvC4) where the director of a videogame company speaks about one of its most successful games. This game is set in a floating city which ...
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157 views
Are Wheeler's It from Bit/Participatory Universe and the Multiverse related?
Could I ask you for the relation between Wheeler's ideas and the multiverse? Do you know if these are related?
I ask you this because I found this very interesting article written by Kip Thorne with ...
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Which physicist is this quote attributed to?
There is a quote from a 19-20th century scientist that goes (and I am paraphrasing):
New scientific theories are never accepted until old scientist die.
Who is this cynical quote attributed to, ...
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Why did Schrödinger write a letter to Einstein “apologizing profusely for his duplicity”?
I’m reading “What is Real” by Adam Becker and this is mentioned without any more details. Here is the excerpt.
(It’s very possible that it refers to something that was mentioned earlier, which I ...
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What actually led Feynman to the path integral formulation of quantum mechanics?
It is commonly known that Feynman's path integral was inspired by Dirac's observation that the kernel is proportional to $\exp{iS/\hbar}$. It was Feynman, however, who had the idea of expressing the ...
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How was the value of the electron's spin ($\pm \frac{\hbar}{2}$) first determined?
The value of the electron's spin is $\pm \frac{\hbar}{2}$.
In the paper where Pauli introduces his Pauli matrices he already knows the value of spin.
I'd imagine it was through the Ster-Gerlach ...
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Did Bohr comment on Bohm's interpretation of quantum mechanics?
Bohm published his interpretation of quantum mechanics in 1952. Comments on Bohm's work from Einstein, Heisenberg und Pauli are cited in the corresponding wikipedia article (https://en.wikipedia.org/...
