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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Why were 20th Century German scientists so impressive?

German (and Austrian) scientists of the late 19th - early 20th centuries seem to have been the backbone of most of modern physics - namely quantum theory/mechanics. The following are a few predominant ...
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How did group theory enter quantum mechanics?

How did the physicists in the 1920s become aware of the importance of group theory in quantum mechanics? Was group theory already part of the physics curriculum at that time, perhaps in connection to ...
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Why did Einstein help in the development of the Quantum theory if he didn't agree with it?

I read the book "A Brief History of Time" By Stephan Hawking. It states that Einstein helped scientists like Pauli etc. in the development of the quantum theory and even shared the Nobel Prize with ...
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Did light bulb companies commission Planck to study black body radiation?

Background When introducing Planck's switch to looking at black-body radiation, a number of sources -- like MinutePhysics, the Economist, random online encyclopaedias and even here on HSM.SE (plus ...
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What was different about Planck's quantization of light compared to Einstein's?

In describing black body radiation Planck assumed that the energy that can be absorbed or emitted by charges is quantized, i.e. they can only absorb or emit certain quantities of energy. But it was ...
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How did quantum mechanics operators come into being?

Now I am starting to learn Quantum Mechanics. In the class I am taught about operators, postulates and all other basic stuff. I understand operators to be +, -, /, etc; but quantum mechanical ...
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Was Dirac really trying to take the square root of the Klein-Gordon operator?

As a student of physics one will, on several occasions, indubitably hear professors or other physicists (here is an example, from Physics.SE's highest-rep user John Rennie) tell the famous story that ...
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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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What is the origin of the “virtual particle pair” metaphor for vacuum fluctuations?

In any layman level description of vacuum fluctuations in quantum field theory the fluctuations are described as a pair of virtual particles spontaneously appearing then disappearing within some short ...
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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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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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How did gyromagnetic ratio come up before quantum mechanics, and who introduced it?

I am really curious about who was the first one to define the gyromagnetic ratio $\gamma$ of a body, i.e. the ratio of its magnetic dipole momento to its angular momentum. It is a very important ...
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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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How did Planck derive the black body radiation formula without using the Bose statistics?

It is so funny that science never develops as in the textbooks. Bose only introduced his statistics in 1924, so Planck could not possibly have used it to derive the radiation formula in 1900. So how ...
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What theories preceded the wave, particles and duality models of light?

Currently, the wave-particle duality model for light is the accepted model. From HyperPhysics: The evidence for the description of light as waves was well established at the turn of the century ...
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Were there serious attempts to model the photoelectric effect classically?

Today we see the photoelectric effect as one of the simplest pieces of empirical evidence that leads to quantum physics. The historical development of the subject, however, seems to have involved much ...
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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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Does anyone know the physics student who passed a quantum mechanics oral exam without taking quantum mechanics?

Many years ago I read an interview with a physics professor, where he recounted a funny situation when he was a graduate student at Harvard. When a first year, he was supposed to take the quantum ...
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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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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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Did wave optics anticipate quantum mechanics?

I heard in wave optics and electromagnetism that Hamilton could have discovered the Schrödinger equation, or that he was the first man who used the expression $$ \Psi(x)= \exp(i S(x)/\hbar)\,. $$ I ...
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Who was the first to say “Shut up and calculate!”?

The best thing I could find on the internet was this apparently forgotten aricle from 12 years ago.
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Were matrix theory and functional analysis well-known to physicists before the invention of matrix mechanics?

Were matrix theory and analysis well-known to physicists circa 1920-1925? Did physicists make extended use of this theory in that period? The question is related to the discussion in How did ...
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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 ...
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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 is the origin of the terminology 'spin up/down'?

In my research area one seminal reference is H. Bethe, ''Zur Theorie der Metalle'', Z. Phys. 71 205 (1931), see also the English translation by T. C. Dorlas (2009). On page 206 of the original ...
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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 did Planck Calculate the Planck Constant?

Having started to learn about quantum behavior, this formula came up: $$E = hf $$ Where $E$ is energy, $h$ is the Planck constant and $f$ is the frequency. My physics teacher suggested an ...
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What was the first journal to have Feynman Diagrams?

I'm writing a paper on the history of Feynman diagrams and am having trouble finding the first paper published by Feynman which features a calculation done with Feynman Diagrams.
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When was the measurement problem solved?

I have been looking into the measurement problem that arises when considering different interpretations of quantum mechanics. Nowadays it seems to be considered a solved problem (in fact some people ...
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Did classical physicists feel ill-at-ease about point charges?

The point charge concept is clearly a very useful mathematical fiction, but it is also problematic from the point of view of "physical intuition". Even a layperson would feel that an explanation is ...
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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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How did quantum mechanics become well known by (non)-scientific community.

Today it is well known even by the non-scientific community that there is a part of physics that deals with the very small called quantum physics. My question is how this became "common knowledge". I ...
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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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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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Who was first to observe or detect photons in the double slit experiment, and how did they do that?

In the early 1800s Thomas Young introduced (a thought-?) experiment also known as the two slit experiment. He discovered the strange way photons created a interference pattern on a screen. There is ...
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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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Einstein's confusion about Stern-Gerlach

In a historical description of the Stern-Gerlach experiment, [Friedrich 2003] says: Einstein and Paul Ehrenfest, among others, struggled to understand how the atomic magnets could take up definite, ...
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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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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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Who first proposed the “colour” charge?

Does anybody know a paper or sorts in which the term "colour" charge in QCD was introduced first? Or any other source in which this label was proposed?
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History of delta barrier in quantum mechanics

I'm interested in finding something out about the history of the problem of the delta potential barrier in quantum mechanics. Which was the first study to propose this problem, and perhaps any ...
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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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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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What came first? The Schrödinger equation or commutation relation between $p$ and $x$

Some books like Griffith's begin quantum mechanics with the Schrödinger equation as a postulate while some other text books derive it and state $[x,p]=i \hbar$ as an axiom. I'm not sure which one came ...
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Why did the “old quantum theory” start off considering circular electron orbits?

It seems that both Bohr and Rutherford assumed circular orbits of electrons around the atom. But why did they do so, instead of assuming e.g. elliptical orbits?
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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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When was the quantization of spin discovered?

When was the fact that a spin could only have values $S = n/2$? I cannot find any source that says when.
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Atomic models in the 1910's and early 1920's [duplicate]

The Rutherford model that invalidated the plum pudding model occured in 1909, while the first model for quantum mechanics was around 1924, leaving a period of 15 years without an adequate model for ...
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Why Doesn't Einstein Get More Credit for Being the Father of Quantum Mechanics?

I'm not simply referring to the notion that Einstein treated the discrete emission and transference of energy (and matter) as "real" physical phenomena, but rather his major continuous role in the ...