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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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 ...
10
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1answer
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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 ...
6
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2answers
672 views

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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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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Can Planck's constant be derived from Maxwell's equations?

Can mathematics (including statistics, dynamical systems,...) combined with classical electromagnetism (using only the constants appearing in chargefree Maxwell equations) be used to derive the Planck ...
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Linearity of quantum mechanics and nonlinearity of macroscopic physics

We live in a world where almost all macroscopic physical phenomena are non-linear, while the description of microscopic phenomena is based on quantum mechanics which is linear by definition. What are ...
14
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1answer
503 views

What is the conclusion from Aharonov-Bohm Effect?

What is the conclusion that we can draw from the Aharonov-Bohm effect? Does it simply suggest that the vector potential has measurable effects? Does it mean that it is a real observable in quantum ...
9
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4answers
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What does a de Broglie wave look like?

What does a de Broglie wave look like? Are de Broglie waves transverse or longitudinal? Can they be polarized? What about the de Broglie wave of a ground state neutral spin-zero Helium 4 atom? ...
7
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1answer
319 views

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 ...
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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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Weyl Ordering Rule

While studying Path Integrals in Quantum Mechanics I have found that [Srednicki: Eqn. no. 6.6] the quantum Hamiltonian $\hat{H}(\hat{P},\hat{Q})$ can be given in terms of the classical Hamiltonian ...
6
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763 views

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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3answers
451 views

Why we use $L_2$ Space In QM?

I asked this question for many people/professors without getting a sufficient answer, why in QM Lebesgue spaces of second degree are assumed to be the one that corresponds to the Hilbert vector space ...
3
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5answers
562 views

Commutator algebra in exponents

Considering $X$ and $Y$ such that $[X,Y]=\lambda$, which is complex, and $\mu$ is another complex number, prove: $$e^{\mu(X+Y)}=e^{\mu X} e^{\mu Y} e^{-\mu^2\lambda/2}$$ My attempt (so far) is: ...
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2answers
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Meaning of the anti-commutator term in the uncertainty principle

What is the meaning, mathematical or physical, of the anti-commutator term? $\langle ( \Delta A )^{2} \rangle \langle ( \Delta B )^{2} \rangle \geq \dfrac{1}{4} \vert \langle [ A,B ] \rangle \vert^{2} ...
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Does every hermitian operator represent a measurable quantity?

In Quantum mechanics, observables are represented by hermitian operator. But does every hermitian operator represent a observable? If not , how do we know that whether a hermitian operator represent ...
8
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2answers
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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 $\Delta x \Delta p \geq \hbar$ ...
8
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2answers
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What is in the space between a nucleus of an atom and its electrons?

There is a common analogy about the structure of an atom, such as the nucleus is a fly in the centre of a sports stadium and the electrons are tiny tiny gnats circling the stadium (tip of the hat to ...
6
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2answers
517 views

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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7answers
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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?

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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3answers
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Matrix elements of momentum operator in position representation

I have two related questions on the representation of the momentum operator in the position basis. The action of the momentum operator on a wave function is to derive it: $$\hat{p} ...
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4answers
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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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652 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.
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2answers
161 views

How exactly does applying the Equipartition Theorem to radiation leads to UV catastrophe?

I'm reading a book by George Gamow, "Thirty years that shook Physics" and have trouble understanding his way of describing the UV catastrophe. In a first part he points out that applying the ...
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5answers
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Is it possible to transfer classical bits of information faster than light speed?

Is there any known, verifiable way to transfer classical information faster than light, using quantum entanglement or other phenomenon? Does quantum teleportation, or other known phenomenon, allow ...
3
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3answers
937 views

Can we have discontinuous wavefunctions in the Infinite Square well?

The energy eigenstates of the infinite square well problem look like the Fourier basis of L2 on the interval of the well. So then we should be able to for example make square waves that are an ...
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1answer
392 views

I am interested in learning Quantum Computing what should I do? [closed]

I wish to learn about quantum computing which seems to be a topic of hot research and overall just intrigues me. I have a strong background in discrete mathematics and number theory. And am a pretty ...
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2answers
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Operators Uncertainty

$\hat A$ is an operator. The uncertainty on $\hat{A}$, $\Delta A$ is defined by: $$\Delta A=\sqrt{\langle\hat A^2\rangle - \langle\hat A\rangle^2}$$ what is difference between $\langle\hat ...
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3answers
756 views

Why is a proton assumed to be always at the center while applying the Schrödinger equation?

Why is a proton assumed to be always at the center while applying the Schrödinger equation? Isn't it a quantum particle?
4
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4answers
306 views

Slit screen and wave-particle duality

In a double-slit experiment, interference patterns are shown when light passes through the slits and illuminate the screen. So the question is, if one shoots a single photon, does the screen show ...
2
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5answers
363 views

Local EPR-experiments with photons in vacuum?

The principle of non-locality states "that an object is influenced directly only by its immediate surroundings." (Wikipedia) When two entangled particles are measured in an EPR experiment, we ...
2
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3answers
972 views

Observation of violation of the uncertainty principle?

I stumbled upon this piece of news in the BBC's website http://www.bbc.co.uk/news/science-environment-19489385, discussing this paper http://prl.aps.org/abstract/PRL/v109/i10/e100404, which reports ...
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3answers
218 views

Does entanglement have a speed or is it instantaneous

The phenomenon of observing one entangled particle and noticing the other take on corresponding values... Does this take a finite speed at all or is it instantaneous?
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2answers
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Is energy exchange quantized?

In the photoelectric effect there is a threshold frequency that must be exceeded, to observe any electron emission, I have two questions about this. I) Lower than threshold: What happen with lesser ...
0
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1answer
191 views

Can Bell's inequality violation be explained by the will of the scientist somehow affecting the experiment?

As far as I know, there are three possible ways to explain violation of Bell's inequality: violation of realism, violation of locality and violation of freedom. The first two are pretty ...
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2answers
587 views

What is the electric field outside a cylindrical solenoid?

What is the electric field outside a cylindrical solenoid when inside is turned on a magnetic field? The question is related to the question aharonov-bohm-effect-electricity-generation
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1answer
155 views

Uncertainty and wave-trains

My textbook and the following extract from feynman's lectures present the same idea regarding wavetrains and uncertainty in their wavelengths. Why is it that a wavetrain confined to some space has an ...
0
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2answers
219 views

What is the required prerequisite knowledge of QM, for starting QFT?

As a physics bsc student, I have a very limited knowledge of QM: Dirac formalism, Schrodinger equation and simple solutions (oscillators, particle in a given potential, hydrogen-like atom etc). There ...
25
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11answers
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Discreteness and Determinism in Superstrings?

So Gerard 't Hooft has a brand new paper (thanks to Mitchell Porter for making me aware of it) so this is somewhat of a expansion to the question I posed on this site a month or so ago regarding 't ...
30
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5answers
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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 ...
35
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4answers
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Trace of a commutator is zero - but what about the commutator of $x$ and $p$?

Operators can be cyclically interchanged inside a trace: $${\rm Tr} (AB)~=~{\rm Tr} (BA).$$ This means the trace of a commutator of any two operators is zero: $${\rm Tr} ([A,B])~=~0.$$ But what about ...
27
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Does a photon interfere only with itself?

I sometimes hear statements like that: Quantum-mechanically, interference pattern occurs due to quantum interference of wavefunction of a photon. Wavefunction of a single photon only interferes ...
12
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5answers
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What is the Physical Meaning of Commutation of Two Operators?

I understand the mathematics of commutation relations and anti-commutation relations, but what does it physically mean for an observable (self-adjoint operator) to commute with another observable ...
33
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4answers
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Does quantum mechanics violate the equivalence principle?

I have a question about equivalence principle in quantum mechanics. Consider a Schroedinger equation under gravitional field $$\left[ - \frac{1}{2m_I} \nabla^2 + m_g \Phi_{\mathrm{grav}} \right]\psi ...
18
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3answers
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Is the universe a quantum computer - is light speed barrier a computational constraint

There is currently a debate ongoing on leading maths blog Gödel’s Lost Letter, between Gil Kalai and Aram Harrow, with the former arguing that building a quantum computer may not be possible due to ...
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4answers
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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 ...
21
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1answer
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In 't Hooft beable models, do measurements keep states classical?

This is a questions on 't Hooft's beable models (see here: Discreteness and Determinism in Superstrings?) for quantum mechanics, and the goal is to understand to what extent these succeed in ...
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Definitions: 'locality' vs 'causality'

I'm having trouble unambiguously interpreting many answers here due to the fact that the terms locality and causality are sometimes used interchangeably, while other times seem to mean very different ...
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3answers
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In what sense is a scalar field observable in QFT?

Consider a QFT consisting of a single, hermitian scalar field $\Phi$ on spacetime (say $\mathbb R^{3,1}$ for simplicity). At each point $x$ in spacetime, $\Phi(x)$ is an observable in the sense that ...
6
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4answers
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Chemical potential

This is something probably very basic but I was led back to this issue while listening to a recent seminar by Allan Adams on holographic superconductors. He seemed very worried to have a theory at ...