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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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?
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 ...
user466
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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
Historically, where did the concept of operators in quantum mechanics come from?
How did people first understand that momentum operator should be of the form of $i \hbar \frac{{\rm d}}{{\rm d}x}$?
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Mathematics motivated by quantum mechanics
It seems that functional analysis is greatly motivated by quantum mechanics, right? Is there any reference on the relation between the two?
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Why did Einstein turn his back on a probabilistic universe?
One of Einstein's famous quotes is "God does not play dice", referring to his dislike of the probabilistic model of the universe, as found by quantum theory. However, in the book "Quantum Mechanics: ...
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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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Etymology of 'qubit'; is there any relation to cubits?
Whilst several not-very-authoritative sources e.g. Wikipedia state that the word qubit was derived, partially, as a play on the word cubit (obviously it also stands for 'quantum bit'), is there any ...
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Stern-Gerlach: oven, or filament?
I've seen conflicting statements about whether the Stern-Gerlach experiment involved an oven to evaporate a sample of silver or a filament, perhaps a filament made of silver. Is it possible that the ...
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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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Einstein and the concept of decoherence
WARNIG: Contrafactual question
It is commonly known that Einstein was not fond of quantum mechanics -- formulated in the famous quote "God does not play dice with the universe".
This quote comes ...
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During the development of QFT was this theory actually used to build any invention like the MRI?
I have always wondered if the equations of quantum field theory were actually ever used in the production of some invention or device other than needed to make predictions about the Standard Model of ...
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What was Einstein's contribution to the Einstein-Podolsky-Rosen (EPR) paper?
Do we have any insight or document into theoretical development of the EPR papers both in terms of math, ideas and anything related to actual physical problem.
I know that Einstein didn't write the ...
Claudio P
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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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Why did Einstein oppose quantum uncertainity?
Einstein always believed that everything is certain, and we can calculate everything. That's why he rejected quantum mechanics, due to its factor of uncertainty. But still quantum physics was right. ...
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History of the fock space based quantization of fields
In almost all Quantum Field Theories textbooks the same approach to quantization is presented as the first example: one considers the scalar real Klein-Gordon field $\phi$ and just write it as
$$\phi(...
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When was the quantization of spin discovered? [duplicate]
When was the fact that a spin could only have values S = n/2 derived? I cannot find any source that says when.
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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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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 is the first effect demonstrating the importance (or existence) of quantum coherence?
As far as I know, in the old quantum theory, a system can only reside in a stationary state. There was no Hilbert space, and no linear superposition. Or, a system cannot be simultaneously in two ...
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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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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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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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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 ...
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Who discovered quanta first, Planck or Einstein? [duplicate]
Planck's 1918 Nobel Prize was awarded
in recognition of the services he rendered to the advancement of Physics by his discovery of energy quanta
in 1900.
However, why do I sometimes see Einstein ...
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Why is harmonic oscillator creation operator called "a-dagger", $a^\dagger$?
As is well known, Dirac introduced the creation and annihilation operators for the quantum harmonic oscillator ($\hat{a}^\dagger$ and $\hat{a}$ respectively), which are now part of every first course ...
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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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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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How did the bra-ket notation become mainstream in quantum mechanics?
I noticed that Dirac bra-kets and their algebra are very much like the linear algebra.
A ket is like a vector, a bra is like the conjugate transpose of a vector, a bra-ket is like a complex inner ...
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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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Who was the first to say "Shut up and calculate!"?
The best thing I could find on the internet was this apparently forgotten article from 12 years ago.
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How did Stern-Gerlach experiment change the concept of space quantization and electron spin?
I got confused by a question which is : "How did Stern-Gerlach experiment change the concept of space quantization and electron spin?" Its the question asked in our ...
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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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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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In explaining photoelectric effect, why is photon quantized and not energy levels of electrons?
Einstein explained the dependence of stopping voltage on photon wavelength by quantizing energy of photon and in his model increasing the intensity will increase the number of photons keeping the ...
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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 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 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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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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Did the concept of the Dirac Sea influence the development of semiconductors like the transistor?
Dirac (1928),
(http://rspa.royalsocietypublishing.org/content/royprsa/126/801/360.full.pdf)
explained the negative-energy solutions of his equations as holes in a sea of electrons.
The concept seems ...
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