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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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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 ...
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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 ...
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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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How did Lie groups work their way into the Standard Model of Particle Physics [duplicate]

In a question answered on this site concerning how group theory worked its way into quantum mechanics it was proposed that this was done by Weyl while investigating the many electron problem. Yes, but ...
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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 ...