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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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 Bohr guessed the quantisation rule?

We all know Bohr's Quantization rule as L=nh/2pi. How did Bohr derive this? If it is a guess, what is the reason behind choosing h/2pi and not some other constant? ...
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175 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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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 $\exp{i\hbar S}$. 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 it was just a mathematical trick to drive 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 ...
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Did Richard Feynman ever meet Stephen Hawking or comment on Hawking radiation?

I was just curious what Richard Feynman thought of Stephen Hawking's Hawking Radiation. Feynman was one of the developers of quantum field theory and Hawking's work would have been cutting edge on the ...
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Einstein really didn't “accept” quantum mechanics? [duplicate]

It is sometimes said that Einstein didn't accept quantum mechanics. Some stronger claims are that he viewed it as wrong altogether, considering it not a viable description of nature. Well, I want to ...
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Who coined the term ''Born's rule''?

Who assigned the term ''Born's rule'' to the statement that the measurement of a quantum observable is one of its eigenvalues, with a probability given by the square of the coefficient in the spectral ...
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How did Pauli come to the Pauli exclusion principle?

I would like to understand what are the ideas (or data) on which the famous scientist has based himself to arrive at such a fundamental principle for quantum mechanics.
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Earliest known usage of letter gamma “Γ” for reducible representation in group theory

Does any know the earliest known usage of the Greek letter gamma for showing a reducible representation of a group? This symbolism is commonly used in character tables in chemical applications of ...
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Pauli's first paper about the spin

Wikipedia states, that the spin degree of freedom was first formulated by Pauli in 1924: In 1924 Wolfgang Pauli introduced what he called a "two-valued quantum degree of freedom" associated with ...
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Who first noted the connection between Heisenberg's Uncertainty Principle and the Fourier Transform?

This is a question about the history of Quantum Mechanics. Who first noted the connection between Heisenberg's Uncertainty Principle and the Fourier Transform?
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What equation is Stephen Hawking most noted for?

I am trying to equate the famous Stephen Hawking to some of our other famous scientists and noted that the vast majority have an associated equation with their name. As for example Einstein was the ...
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Why is the azimuthal quantum number so named?

The name "azimuthal quantum number" is often used for the total orbital angular momentum quantum number $\ell$ in an atom. What is the origin of this name? It makes no sense to me, since the usual ...
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How did Born come up with the Canonical Commutation relation ($\hat X \hat P-\hat P\hat X=i\hbar$)?

All answers to questions like this dodge the question by saying it's a postulate of Matrix Mechanics, so let me rephrase it. Instead of how to derive the CCR, how does it follow from Heisenberg's ...
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Why is the angular momentum written as JJ in quantum mechanics?

Why is $\textbf{J}$ called angular momentum operator? Can anyone explain why the expectation value of J is angular momentum? Here is how $J$ is defined: The rotation operator $$ U(\alpha)=\exp(-i {\...
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Photon interpretation of G.I. Taylor's diffraction of feeble light

In 1909, Cambridge undergraduate G.I. Taylor published a letter describing his observation of diffraction using light of an extremely low intensity. For years, I've been teaching my students the ...
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Are there any records that show how Hilbert came to “invent” or “discover” Hilbert spaces?

I think it's fuzzy as to whether or not this question is appropriate to ask on this site. The reason I ask it that the characteristics of Hilbert spaces are very much used in expressing quantum ...
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Who did enunciate each postulate of modern Quantum Mechanics

Nonrelativistic Quantum Mechanics (QM) relies in a number of postulates and although some authors may disagree about the exact set, there are a few which are quite indisputable: States are ...
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Origin of operators in quantum mechanics

From where did the concept of operators in quantum mechanics come, historically? How did people first understand that momentum operator should be of the form of $i\hbar\,{\rm d}/{\rm d}x$? Also how ...