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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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37 views

Who introduced the fermionic creation and annihilation operators?

It is strange that this is never mentioned when textbooks introduce the 2nd quantization formalism.
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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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I want to know the tricks to search for and find old academic journals for free

In the research of scientific and mathematical history, efficient skills in searching for and accessing old academic journals (preferably for free) are essential. However, even when using platforms ...
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Is the first paper attempting to apply Hilbert space theory to quantum mechanics in 1926 Germany available for free online?

I would like to view the quantum mechanics paper "Über die Jacobischen Transformationen der Quantenmechanik," published in Germany in 1926 by Fritz Wolfgang London. The reference is Z. Phys. ...
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Early helium spectrum measurements and their challenge for Bohr's quantum mechanics

My understanding is that explaining ortho- and para- helium spectral lines was a key motivation for Heisenberg's new quantum theory. For example, Birthwistle's 1928 "The New Quantum Mechanics&...
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Was Bell’s theorem historically seen as evidence against realism and determinism?

As Tim Maudlin points out in his paper: Early on, Bell’s result was often reported as ruling out determinism, or hidden variables. Nowadays, it is sometimes reported as ruling out, or at least ...
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I'm searching for the original paper from 1924 where Max Born first proposed the term "quantum mechanics."

I'm searching for historical documents pertaining to quantum mechanics because I aim to write a popular essay on the topic for a web magazine. Specifically, I'm seeking free access to Max Born's paper ...
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Use of eigenvalues of operators in quantum mechanics

My very basic understanding of Quantum Mechanics and its history is that first, some physical quantities were thought to be continuous but experiments showed that they only took discrete values. My ...
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Origin of Einstein quote "Quantum mechanics: Real Black Magic Calculus"

The description of the 1993 English translation of The Quantum Dice, by Ponomarev and Kurchatov, as well as one of the quotes for chapter 2 of Quantum Computation and Quantum Information, by Nielsen ...
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What paper or papers about molecules did Heisenberg "like", and what has Heisenberg published or otherwise commented about it?

In the 2023 film Oppenheimer based on the 2005 biography American Prometheus by Kai Bird and Martin J. Sherwin, there seems to be two references to work by Oppenheimer on molecules: RABI: I caught ...
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A brief history of "delocalization" of electrons

I have been studying the concepts of "resonance" and "mesomerism" recently and a common principle of these concepts is the "delocalization" (of electrons, molecular ...
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Origin of the name "Loschmidt echo" in quantum chaos studies

The name "Loschmidt echo" is used in quantum physics for the quantity $$ M(t) \equiv \left| \langle\psi_0| e^{i H t/\hbar} e^{-i H_0 t/\hbar} |\psi_0\rangle \right|^2 $$ where $$ H = H_0 + ...
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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 2004: N. David Mermin, Could Feynman have said this?, Physics Today 57 (5), 2004.
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On the naming of quantum chromodynamics

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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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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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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Dirac’s debt to Hamilton

According to Tobias Hurter’s popular exposition Too Big for a Single Mind (narrated in the present tense): Dirac makes use of an elegant mathematical tool developed by the Irish mathematician William ...
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How did Schrödinger do quantum mechanics with wave functions?

On my way to learn about the very beginning of quantum mechanics and its different formulations, starting with Heisenberg infinite matrices and Schrödinger's wave functions, I can really not find till ...
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Why was the Greek letter psi (Ψ) chosen to represent the wave function?

When I was reading, the question just popped into my head after noticing that the Greek letter ψ looks kind of like a wave itself. Stylized, they look even more wavy: $$\Huge \Psi\;\Huge\psi$$ This ...
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Does the prototype BB84 quantum cryptography machine still exist?

According to Wikipedia's timelines, quantum computing may have had some inceptions as early as the late 60's, when Stephen Wiesner invented conjugate coding. Around the early 80's, Wiesner's ideas ...
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Who was the scientist who first showed that helium has a bound state, and was he a nazi?

I remember from my quantum course that the first person (I believe in 1927) to show that helium has a bound state, using the variational principle, was a nazi. It was remarked by my professors that he ...
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Who was the first to make a Stern-Gerlach experiment with two magnets?

I'm trying to fill a conceptual gap I have in the history of physics In 1922 Stern and Gerlach make their experiment, proving that electrons have intrinsic angular momentum, however it takes a while ...
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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 Heisenberg say free will could arise from quantum probabilistic mechanics?

I see this view attributed to him a lot during Twitter debates but I never found the source for it does anyone know if Heisenberg actually held this view/suggested it?
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Did any "classical era" physicist foresee that a theory such as Quantum Mechanics is logically inescapable?

I am interested in knowing if in the era preceding the observations that lead to the advent of Quantum Mechanics, anyone foresaw logically that a theory such as Quantum Mechanics is in a sense, "...
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How and by whom was the magnetic term in the Hamiltonian first derived?

The Hamiltonian of a charged particle in a magnetic field is: $$H=\frac{1}{2m}(\frac{h}{2\pi i}\nabla-qA)^2+q\phi$$ Can anybody help me find out when, how and by whom was it first derived?
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Who popularized the atom icon (atomic whirl or planetary model)

There is a symbol or icon for an atom that is instantly recognizable and is associated with nuclear physics and with chemistry. A search for "nuclear atom symbol" (on 3/23/2023) shows what ...
2 votes
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Whom did Sommerfeld prefer as student?

On the occasion of Heisenberg's death, Wigner wrote an obituary in April 1976 issue of Physics Today (pp. 86-87): Sommerfeld, an excellent teacher with a wonderful overall knowledge of his discipline,...
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Understanding how Stern-Gerlach tests Bohr-Sommerfield Hypothesis

I am trying to get to the bottom of a few things in the Stern-Gerlach experiment. First, on wikipedia, it says The Sommerfeld model predicted that the magnetic moment of an atom measured along an ...
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1 answer
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From where did Heisenberg (1925) obtain the classical frequency equation?

In Quantum-Theoretical Re-Interpretation (1925), Heisenberg gives the following: In order to characterize this radiation [of an electron] we first need the frequencies which appear as functions of ...
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Why are the views of quantum mechanics called the Copenhagen School?

Why was the name of a group of opinions about the meaning of quantum mechanics called the Copenhagen Interpretation, relative to the Danish city of Copenhagen and not the name of a scientist named ...
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Who first stated the three polarizers experiment in quantum mechanics?

In my experience, Dirac is most often cited as the origin of this thought experiment. However, from what I've read in his Principles of Quantum Mechanics, he never actually introduces the idea with ...
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Why is 'total angular momentum' denoted by the letter $J$ in quantum mechanics?

In quantum mechanics, we say $J$ ('total angular momentum') = $L$ ('orbital angular momentum') + $S$ ('spin angular momentum'). Apparently $S$ is from 'Spin', but why $J$ for the total angular ...
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question regarding Stern-Gerlach experiment

When Stern-Gerlach experiment was done with quantum electron , two peaks were observed rather than a continuous distribution as in case of small magnets , but how did those peaks confirm that angular ...
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Paradigms in Newtonian physics around 1900

I am thinking about the change from Newtonian mechanics to quantum physics and relativity. I note that we have accepted the words "ultraviolet catastrophe" in connection with the situation ...
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What did Einstein say about the Dirac equation?

The wiki article on Dirac quotes Einstein as saying of Dirac I have trouble with Dirac. This balancing on the dizzying path between genius and madness is awful. and I don't understand Dirac at all. ...
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What did Nathan Rosen (from EPR) say about Bell's inequality and its violation?

Motivated by this year's Nobel prize in physics, I was wondering whether there are recorded statements by Nathan Rosen (the R in the EPR-paradox) about the Bell inequality and its violation by this ...
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Why was Alain Aspect discouraged from doing his now Nobel-winning work?

In an interview following Aspect's winning of the Nobel Prize in Physics, he claims that John Stuart Bell discouraged him from pursuing his now-famous 1982 experiment on quantum entanglement. The ...
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What's the early history of the "inner quantum number"?

Pais, in his "Inward Bound", describes the early history of spin. He tells us that Goudsmit and Uhlenbeck interpreted Pauli's "doubled valuedness" as spin, while in turn Pauli re-...
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What are the favorite interpretations of quantum mechanics by the recent Nobel laureates in physics?

The new Nobel laureates in physics have been given the prize because of their contributions to quantum mechanics (QM). Of course, the Nobel prize focusses more on groundbreaking work that has links to ...
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What is the origin of the name "degeneracy" pressure and "degenerate" Fermi gas?

What is the origin of the name "degeneracy" pressure and "degenerate" Fermi gas? I was trying to find the first paper that used the term "degenerate/degeneracy" to ...
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According to Heisenberg, is quantum theory merely a calculation procedure for predictions?

Is quantum theory just a mathematical tool for correct predictions, according to Heisenberg's views? What are his personal ontological commitments in relation to quantum theory (if he had any ...
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Did John von Neumann make any comments about the Many Worlds Interpretation of Hugh Everett?

I was having a discussion with a physicist about Many Worlds Interpretation and he told me that von Neumann like the idea of having multiple worlds in quantum mechanics. When I asked him about more ...
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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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Did Felix Bloch really discover Bloch oscillations?

A 1929 paper by Felix Bloch, Über die Quantenmechanik der Elektronen in Kristallgittern, is widely cited as having predicted the phenomenon of Bloch oscillations: The oscillatory motion of an electron ...
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The original Dirac equation

In the original 1928 paper (pdf) the Dirac equation appears on page 615 in equation (9) as $$ [p_0+\rho_1\left(\boldsymbol{\sigma},\boldsymbol{p}\right)+\rho_3mc]\psi=0\qquad(1) $$ Using the ...
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de Broglie's conception of the electron

I've been working on de Broglie's thesis (English PDF, Original French PDF) for a course, and I've found something that's been bothering me. My training is in Physics, and so I'm not particularly ...
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Einstein's overdetermination theory

In 1923 [1], Einstein proposed an idea for a classical theory that would explain some features of quantum mechanics, via the overdetermination of the EoM, so that only certain configurations would be ...
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On implications of Schrodingers Cat regarding macroscopic quantum states and decoherence

How exactly did Schrodingers Cat lead to development regarding macroscopic quantum states and decoherence? One often hears that the thought experiment was the initiator to the question, whether ...
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Origin of the recurrence relation for Clebsch-Gordan coefficients

The Clebsch-Gordan coefficients $C_{\pm }(J,M)$ arise in quantum mechanics in the problem of addition of angular momentum. They also arise in mathematics in the more theoretical (but related) problem ...