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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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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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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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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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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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 ...
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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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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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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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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 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'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 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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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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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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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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What did Schroedinger try to say with the cat thought experiment?
In many books one finds different explanations. Specifically popular seems to be that he "argued against the Copenhagen interpretation". But what did he really intend to communicate?
I for ...
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Einstein's Objection to Drude Model
In Walter Isaacson's Biography of Einstein, it is stated that the young Einstein was developing his own ideas in Statistical Physics and Thermodynamics and he had found some error in Drude's model for ...
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Who was the first scientist to give a formula for the probability density function of the position of a photon in the double slit experiment?
The double-slit experiment shows the fundamentally probabilistic nature of quantum mechanical phenomena. On Wikipedia one can read:
This type of experiment was first performed, using light, by Thomas ...
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How did Heisenberg build the P Q matrix terms?
I learnt in some Wikipedia articles that the terms of the P and Q matrices designed by Heisenberg were composed of Fourier coefficients. Could you provide some explanation on how these coefficients ...
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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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Who first proposed the idea of "resolution of the identity"?
Who first proposed the idea of "resolution of the identity" as used in the functional calculus of self-adjoint operators? Was it von Neumann?
In Japanese, it translates as "resolution ...
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What technology was used to determine the shape of the blackbody spectrum at the 19th century?
The shape of the blackbody radiation spectrum was known in the 19th century from experimental measurements, and before the theoretical discovery of Planck's law.
At those times, how did people manage ...
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How did Stern or Gerlach, of Stern-Gerlach experiment, create individual silver atoms? How were they accelerated?
How, a century ago, could Stern and/or Gerlach KNOW that they had created single silver atoms?
How were they moved, or accelerated?
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Bohr-Kramers-Slater (BKS) theory and energy conservation only on statistically basis
I was reading Wikipedia article on Bohr-Kramers-Slater (BKS) theory, https://en.wikipedia.org/wiki/BKS_theory. I encountered two interesting points and need your help to understand the reasons behind ...
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Need quote from early 20th century about humanity probably never being able to control (manipulate, see?) a single quantum system
I remember having read a statement, I think by one of the founding fathers of quantum mechanics, that we will probably never be able to control (or manipulate or see or isolate...?) a single quantum ...
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On the origin of "sandwiches" in quantum mechanics
The term "sandwich" and the verb "to sandwich" appear pretty common but informally in quantum mechanics. Generally when describing some kind of inner product of the form:
$$\langle ...
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Why are pilot waves in quantum mechanics said to be Faraday waves?
De Broglie proposed a pilot wave in connection with quantum mechanics. He was more or less forced to abandon this wave in favor of the Copenhagen view. Bohm furthered his approach in the fifties but ...
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Why didn't the phase space formulation of Quantum Mechanics get the upper hand?
At university I learned quantum mechanics in or position or momentum variables. Later (in fact on this site), I learned about the phase space formulation in which both are used at the same time.
The ...
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What is the origin of the probability interpretation of quantum mechanics?
Born came up with his probability interpretation of quantum mechanics. But why did he think about such an interoretation? Why not thinking that a deterministic process has to lay at its foundation? ...
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Why did the Copenhagen interpretation of quantum mechanics got the upperhand?
The Copenhagen interpretation of quantum mechanics is nowadays the interpretation that prevails over other interpretations (or theories). Basically, it states that all processes in Nature are ...
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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 ...
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A technical and historical introduction to quantum mechanics
I am curious to understand the history of QM. In particular, how did the physicists conclude that observables can be treated as operators, or the use of complex state spaces, or that Eigenvalues of ...
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Was Landau interested in the interpretations of quantum mechanics?
I am interested in Lev Landau. I was trying to find what was his approach to the interpretation of quantum mechanics, I am unable to find any particular source were this is discussed.
Was he an ...
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What are the definitive experiments/phenomena which motivate quantum mechanics?
The double slit experiment is usually given as the foremost example of a physical experiment that requires quantum mechanics to satisfactorily explain. However, every account i've seen of it (such as ...
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