Quantum mechanics describes the microscopic properties of nature in a regime where classical mechanics no longer applies. It explains phenomena such as the wave-particle duality, quantization of energy and the uncertainty principle and is generally used in single body systems. Use the ...

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Is Stephen Wolfram's NKS, an attempt to explain the universe with cellular automata, in conflict with Bell's Theorem?

Stephen Wolfram's A New Kind of Science (NKS) hit the bookstores in 2002 with maximum hype. His thesis is that the laws of physics can be generated by various cellular automata--simple programs ...
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How can one derive Schrödinger equation?

The Schrödinger equation is the basis to understanding quantum mechanics, but how can one derive it? I asked my instructor but he told me that it came from the experience of Schrödinger and his ...
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Why is the contribution of a path in Feynmans path integral formalism $\sim e^{(i/\hbar)S[x(t)]}$

In Feynman's book "Quantum Mechanics and Path Integrals" Feynman states that the probability $P(b,a)$ to go from point $x_a$ at time $t_a$ to the point $x_b$ at the time $t_b$ is $P(b,a) = ...
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Meaning of inner product $\langle \vec{r} | \psi(t)\rangle $

I have come across the equation which comes out of the nothing in Zettili's book Quantum mechanics concepts and applications p. 167: $$\psi(\vec{r},t) ~=~ \langle \vec{r} \,|\, \psi(t) \rangle.$$ ...
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What is a phonon?

I am trying to understand intuitively what a phonon is, but for the moment I find it quite difficult (having a limited background in quantum mechanics, an undergraduate course in non-relativistic QM). ...
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Are there any theoretical limits on the energy of a photon?

Is there any lower or upper limit on the energy of a photon? i.e. does the mathematical framework we currently use for Quantum Mechanics blow up when a photon surpasses a certain upper limit of ...
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Applications of the Spectral Theorem to Quantum Mechanics

I'm currently learning some basic functional analysis. Yesterday I arrived at the spectral theorem of self-adjoint operators. I've heard that this theorem has lots of applications in Quantum ...
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Is Gravity an entropic force after all?

Recently, there was a rapid communication published in Phys.Rev.D (PRD 83, 021502), titled "Gravity is not an entropic force", that claimed that an experiment performed in 2002 with ultra cold ...
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Galilean invariance of the Schrodinger equation

I am only asking this question so that I can write an answer myself with the content found here: http://en.wikipedia.org/wiki/User:Likebox/Schrodinger#Galilean_invariance and here: ...
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Dimension of Dirac $\gamma$ matrices

While studying the Dirac equation, I came across this enigmatic passage on p. 551 in From Classical to Quantum Mechanics by G. Esposito, G. Marmo, G. Sudarshan regarding the $\gamma$ matrices: ...
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Difficulties with bra-ket notation

I have started to study quantum mechanics. I know linear algebra,functional analysis, calculus, and so on, but at this moment I have a problem in Dirac bra-ket formalism. Namely, I have problem with ...
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The Many Body problem

(This is a simple question, with likely a rather involved answer.) What are the primary obstacles to solve the many-body problem in quantum mechanics? Specifically, if we have a Hamiltonian for a ...
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Once a quantum partition function is in path integral form, does it contain any operators?

Once a quantum partition function is in path integral form, does it contain any operators? I.e. The quantum partition function is $Z=tr(e^{-\beta H})$ where $H$ is an operator, the Hamiltonian of the ...
13
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What exactly are Hamiltonian Mechanics (and Lagrangian mechanics)

What exactly are Hamiltonian Mechanics (and Lagrangian mechanics)? I want to self-study QM, and I've heard from most people that Hamiltonian mechanics is a prereq. So I wikipedia'd it and the entry ...
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Quantization of a particle on a spherical surface

Suppose we have a particle of mass $m$ confined to the surface of a sphere of radius $R$. The classical Lagrangian of the system is $$L = \frac{1}{2}mR^2 \dot{\theta}^2 + \frac{1}{2}m R^2 \sin^2 ...
13
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Born rule for photons: it works, but it shouldn't?

We can observe double-slit diffraction with photons, with light of such low intensity that only one photon is ever in flight at one time. On a sensitive CCD, each photon is observed at exactly one ...
12
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What does John Conway and Simon Kochen's “Free Will” Theorem mean?

The way it is sometimes stated is that if we have a certain amount of "free will", then, subject to certain assumptions, so must some elementary particles."(Wikipedia) That is confusing to me, ...
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What is the relation between position and momentum wavefunctions in quantum physics?

I have read in a couple of places that $\psi(p)$ and $\psi(q)$ are Fourier transforms of one another (e.g. Penrose). But isn't a Fourier transform simply a decomposition of a function into a sum or ...
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714 views

Quantum mechanics in a metric space rather than in a vector space, possible?

Quantum mechanics starts with wave functions living in Hilbert space. But later for Born's interpretation, the wave function need to be of unit energy (I mean total probability = 1, ...
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Negative probabilities in quantum physics

Negative probabilities are naturally found in the Wigner function (both the original one and its discrete variants), the Klein paradox (where it is an artifact of using a one-particle theory) and the ...
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8answers
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Why do quantum physical properties come in pairs?

Why do quantum physical properties come in pairs, governed by the uncertainty principle (that is, position and momentum?) Why not in groups of three, four, etc.?
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Why is the second order perturbative correction to the ground state energy always down?

What is the physical/deeper reason for the second order shift of the ground state energy in time independent perturbation theory to be always down? I know that it follows from the formula quite ...
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Has a double slit experiment ever been done using a track chamber or even contemplated?

I tried searches and the question has been posed in other fora, but no experiment came up. Track chambers (cloud chambers, bubble chambers , time projection chambers, solid state detectors like the ...
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Definite Parity of Solutions to a Schrödinger Equation with even Potential?

I am reading up on the Schrödinger equation and I quote: Because the potential is symmetric under $x\to-x$, we expect that there will be solutions of definite parity. Could someone kindly ...
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What are the specific requirements for a do-it-yourself quantum double-slit experiment?

I was shocked to recently learn that the double-slit experiment is not only possible to do with completely ordinary equipment (with photons of course), but it actually looks rather easy. This is from ...
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Why don't quantum effects invalidate the speed of light barrier?

While proving that no matter can reach the speed of light (a fact which I call the kinetic energy barrier), Einstein uses the fact that he can calculate the velocity and position of an electron. ...
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Does magnetic monopole violate $U(1)$ gauge symmetry?

Does a magnetic monopole violate $U(1)$ gauge symmetry? In what sense and why? Insofar as I know, there are at least two types of magnetic monopoles. One is the Dirac monopole while the other is the ...
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Does the mass of an electron change with its “energy state”?

When an electron absorbs a photon, it gets into a higher energy state and goes into the upper orbit/shell. Does (rather should) this absorption of energy also have an impact on its mass (although ...
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Is the collapse of the wave function inherently time asymmetric?

Schroedinger's equation, as we all know, is time symmetric. In quantum field theory, we have to come up with a more sophisticated CPT reversal, but the essential point remains unchanged. However, the ...
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Double connectivity of $SO(3)$ group manifold

Is there any physical significance of the fact that the group manifold (parameter space) of $SO(3)$ is doubly connected? EDIT 1: Let me clarify my question. It was too vague. There exists two ...
6
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Does the canonical commutation relation fix the form of the momentum operator?

For one dimensional quantum mechanics $$[\hat{x},\hat{p}]=i\hbar $$ Does this fix univocally the form of the $\hat{p}$ operator? My bet is no because $\hat{p}$ actually depends if we are on ...
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Does String theory say that spacetime is not fundamental but should be considered an emergent phenomenon?

Does String theory say that spacetime is not fundamental but should be considered an emergent phenomenon? If so, can quantum mechanics describe the universe at high energies where there is no ...
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Are quantum mechanics calculations useful for engineering?

I heard it's is pretty tough to get results for more than a few quantum particles. Are quantum mechanical calculations useful at all for any technology that is being sold? Or do they use ...
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Probability and probability amplitude

The equation: $$P = |A|^2$$ appears in many books and lectures, where $P$ is a "probability" and $A$ is an "amplitude" or "probability amplitude". What led physicists to believe that the square of ...
2
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1answer
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What is the physical importance of the commutation relations of angular momentum?

What is the physical meaning of these commutation relations: $$[L_{z},L_{\pm}]=\pm\hbar L_{\pm}\tag{1}$$ and $$[L_{+},L_{-}]=2\hbar L_{z} ~?\tag{2}$$
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The transactional interpretation of quantum mechanics

John Cramer’s transactional interpretation of quantum mechanics (TIQM) is billed as resolving the fuzzy agnosticism of the Copenhagen interpretation while avoiding the alleged ontological excesses of ...
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Is there a maximum possible acceleration?

I'm thinking equivalence principle, possibilities of unbounded space-time curvature, quantum gravity ...
10
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The strange thing about the maximum in Planck's law

I read that it makes a difference whether you calculate $\frac{dE(\lambda) }{d \lambda}=0$ or $\frac{dE(\omega)}{d \omega}=0$ in the sense that the maximum energy density with respect to the ...
8
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Heisenberg Uncertainty Principle: Which formula is correct?

Some websites and textbooks refer to $\Delta x \Delta p \geq \frac{\hbar}{2}$ as the correct formula for the uncertainty principle whereas other sources use the formula $\Delta x \Delta p \geq \hbar$ ...
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What exactly is the 'observer' in physics and/or quantum mechanics? [duplicate]

Possible Duplicate: nature of an observer For instance, in the double slit experiment, what is exactly defined as an observer? I remember from somewhere, light is also an observer?
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What keeps electrons in an atom from flying away or falling into the nucleus?

In atoms, what force or charge, etc. keeps electrons from flying away or into their nucleus? is there a kind of weak-force at work on the atomic scale? Note I am aware the electron positions are ...
2
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3answers
684 views

Who is doing the normalization of wave function in the time evolution of wave function?

In the Schrodinger equation, at any given time $t$ we should jointly add another sub equation, like $$||\psi_t(x)|| = 1$$ where $\psi_t(x) = \Psi(x,t)$, and then try to solve the two equations ...
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877 views

Mathematics for Quantum Mechanics [duplicate]

What math should I study if I want to get a basic understanding of quantum mechanics and especially to be able to use the Schrodinger's equation.
8
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Partition function containing QM?

I am wondering about the partition function of the classical microcanonical ensemble. It contains Planck's constant and also an indistinguishability argument about the particles I am looking at and I ...
8
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878 views

Quantum entanglement and spooky action at a distance

When quantum entanglement is explained in "layman's terms", it seems (to me) that the first premise, that we have to accept on faith, is that a particle doesn't have a certain property (the particle ...
7
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Many-worlds: how often is the split how many are the universes? (And how do you model this mathematically.)

When I read descriptions of the many-worlds interpretation of quantum mechanics, they say things like "every possible outcome of every event defines or exists in its own history or world", but is this ...
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Is the universe finite and discrete?

Is the universe finite, both in the sense of being a closed spacetime manifold, as viewed from the macro level, but also in the sense of being fully discrete and finite in all of its intricate quantum ...
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Why is Heisenberg's uncertainty principle not an experimental error since it is the error created by photons striking on elementary particles? [duplicate]

Why is Heisenberg's uncertainty principle not an experimental error since it is the error created by photons striking on elementary particles?
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proof for $\langle q| p \rangle = e^{ipq}$

What would be the proof for $\langle q| p \rangle = e^{ipq}$? Is it derived from canonical commutation relation? ($|q \rangle $ represents the position eigenstate, while $|p \rangle$ represents the ...
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Bohr Model of the Hydrogen Atom - Energy Levels of the Hydrogen Atom

Why the allowed (stationary) orbits correspond to those for which the orbital angular momentum of the electron is an integer multiple of $\hbar=\frac {h}{2\pi}$? $$L=n\hbar$$ Bohr Quantization rule of ...