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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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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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 here https://en.wikipedia.org/wiki/Self-energy ?
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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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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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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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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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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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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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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/...
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Which is the physical interpretation of the “strange” constant $e \cdot c/ 4 \pi$?

This constant is assignable to charged leptons $(e, \mu, \tau)$ representing the fraction of their individual magneton $\hat{m}= e \cdot \hbar/ 2 m$ to their Compton-wavelength $\lambda_{C} = h / m ...
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What new physics was discovered or needed as a result of the Manhattan Project?

I originally asked this question on the Physics StackExchange and was told to migrate it here. I've tightened up the question a bit. I recently got into a discussion with colleagues regarding ...
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Degenerate States in Quantum Mechanics

In his book on quantum mechanics in the chapter on perturbation theory Dirac says in a footnote: A system with only one stationary state belonging to each energy-level is often called non-...
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Planck's quantization idea

First of All, I doubt there has ever been any new idea that did not involve intuition. However, most textbooks suggest that the quantization idea was just a mathematical trick, that Planck introduced ...
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About the quantum mechanical relation $\:qp-pq= \mathrm{i}\hbar I\:$ [closed]

Could I argue that the quantum mechanical relation "discovered" by Heisenberg \begin{equation} qp-pq= \mathrm{i}\hbar I \tag{01}\label{01} \end{equation} is the greatest scientific discovery of ...
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Distinguishability of particles in statistical mechanics

Historically,how,and by what experiments,the concept of identical and distinguishable particles was discovered?Is it a tagline set by scientists,or nature indeed works in this way?
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Max Planck and energy quantization idea

Did Planck have an intuition behind the idea of energy quantization of atomic oscillators and radiation, or was it just a mathematical trick to derive his distribution law?
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Who solved the quantum harmonic oscillator?

In continuation of this question, Who introduced the creation and annihilation operators for the harmonic oscillator?, I got curious who came up with the quantum harmonic oscillator originally. I am ...
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Who solved the particle-in-a-box model first?

I got curious who invented the particle-in-a-box model first. It is really simple and intuitive. I was googling to find the original author who suggested it but I only get textbook or webpages as ...
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How to understand `After quantum mechanics, nature itself suddenly became linear`?

How to understand Freeman Dyson's Saying: After quantum mechanics, nature itself suddenly became linear.
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Why did Schrödinger choose a cat for his thought experiment?

While Schrödinger's cat thought experiment serves a greater purpose than animal cruelty enjoyment, one of the possible results is a dead cat. Gruesome or not is one's appreciation, but you will ...
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Did Sommerfeld derive or measure the fine structure constant the first time he introduced it?

I used Wikipedia to try to figure this out but I am not clear on the explanation. As for Newton's Law of Gravitation does not give the value for the Gravitational constant but it was measured by ...
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Historically how it was discovered that we need fields to describe matter?

This question is from one historical perspective. The question is: how physicists historically found out that one needs quantum fields to describe matter? Being more detailed. Let us consider the ...
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What is the history and motivation for the (d-1,1) notation used to describe a field theory?

Very often in the literature of research papers and other articles, and maybe text books, on topics of quantum field theory, a theory may be described as a 3+1 or 0+1, or maybe even 1+1 theory. I ...