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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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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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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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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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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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'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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Understanding Bohr's response to a 1930 Einstein thought experiment that challenged the uncertainty principle
Structure of this post
I want to better understand how Bohr responded to Einstein's 1930 attempt to demonstrate that quantum mechanics was inherently contradictory under the Copenhagen interpretation....
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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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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 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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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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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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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 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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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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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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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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Background on the Stone-von Neumann theorem
I'm a mathematician.
I'm required to give a lecture on the Stone-von Neumann theorem. I already have all the mathematical details figured out, but I wish to make the lecture more interesting by giving ...
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Did Rydberg ever learn of Bohr's quantum-mechanical explanation of his formula?
The Rydberg formula on the wavelengths of a spectral line in chemical elements was first stated empirically in 1888 by Johannes Rydberg. A theoretical explanation of the formula wouldn't arive until ...
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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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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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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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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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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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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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Dirac's non-neglibile disturbances argument and epistemic quantum mechanics
Here is Dirac's argument about one reason to motivate quantum mechanics:
"It is usually assumed that, by being careful, we may cut down the disturbance accompanying our observation to any desired ...
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How did Bohr guess the quantization rule?
We all know Bohr's quantization rule as $L = \frac{nh}{2\pi}$. How did Bohr derive this?
If it is a guess, what is the reason behind choosing $\frac{h}{2\pi}$ and not some other constant? Why did he ...
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Did Werner Heisenberg ever agree or propose the existence of some kind of multiverse?
I was watching a video (https://www.youtube.com/watch?v=muJYTeQlvC4) where the director of a videogame company speaks about one of its most successful games. This game is set in a floating city which ...
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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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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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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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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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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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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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Did the mathematician Garrett Birkhoff ever work with or mention Feynman's path integrals?
Did Garrett Birkhoff ever work with Feynman's path integral? Did he ever work in his Many-Histories interpretation? Or at least, did he mention it in any of his articles?
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Did Einstein or the scientific community know about quantum tunneling during the EPR debates?
It is my understanding that Einstein produced the EPR paper to necessarily elucidate the existence of physical properties that could not exist prior to measurement. That was his assumption which was ...
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What did Hans Bethe think of von Neumann's quantum logic?
Nobel laureate Hans Bethe was a friend of mathematician-physicist John von Neumann, and he once said:
"I have sometimes wondered whether a brain like von Neumann's does not indicate a species ...
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Which is the physical interpretation of the "strange" constant $e \cdot c/ 4 \pi$?
This constant is assignable to charged leptons $(e, \mu, \tau)$ representing the fraction of their individual magneton $\hat{m}= e \cdot \hbar/ 2 m$ to their Compton-wavelength $\lambda_{C} = h / m ...
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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 was it just a mathematical trick to derive his distribution law?
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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 {\...
user6964
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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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