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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272 views

Finding the energy eigenvalues of Hydrogen using WKB approach

I need help to find the energy eigen values of Hydrogen atom using WKB approach. So far I know, the radial equation is given by $$\frac{1}{r^2} \frac{\partial }{\partial r} \left( r^2 \frac{\partial ...
8
votes
3answers
639 views

Spontaneous symmetry breaking in classical mechanics, quantum mechanics and quantum field theory

I wondered if someone could help me understand spontaneous symmetry breaking (SSB) in classical mechanics, quantum mechanics and quantum field theory. Consider a Higgs-like potential, with a local ...
-1
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1answer
159 views

Commutator with Pauli spin matrices and the momentum operator

How is $\left[\vec\sigma \cdot \vec p, \vec \sigma \right]$ proportional to $\vec \sigma\times \vec p$, where $\sigma$ are the Pauli spin matrices and $p$ is the momentum operator?
0
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1answer
111 views

Wavefunction Problem wrong in solutions manual? [closed]

Well there is a problem in my book which lists this problem: Calculate the probability that a particle will be found at $0.49L$ and $0.51L$ in a box of length $L$ when it has (a) $n = 1$. Take the ...
0
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2answers
70 views

Quantum Mechanical States

What can be the precise answer to the question that Quantum states are complex and infinite dimensional. Why is this so? Is it because they belong to the complex Hilbert space? Even if they ...
0
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1answer
42 views

Amateur thoughts on QM theory at celestial scale

Some amateur scientist asked me that why can't one just simply apply the entire theory of QM at atomic scale to "quantize" celestial system with a different choice of $\hslash$, which he believed can ...
2
votes
3answers
95 views

Angular momentum eigenstates

My textbook says that if $L^2$ is the square of the angular momentum and if it's eigenstate is $|\alpha,\beta>$ then its eigenvalue is $\hbar^2\alpha$ i.e. ...
1
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1answer
104 views

What does the magnetic field of the (quantum-mechanical) electron look like?

While a treatment of electron spin can be found in any introductory textbook, I've noticed that the electron's magnetic field seems to be treated classically. Presumably this is because a quantum ...
5
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1answer
30 views

Is the subadditivity of quantum entropy valid in the infinite-dimensional case?

Does the subadditivity (and strong subadditivity) of quantum entropy hold for infinite dimensional quantum systems as well? Unfortunately the books in my hand give proof for finite dimensional cases ...
3
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1answer
92 views

Instantons in Witten's supersymmetry and Morse theory

I'm reading Witten's paper on supersymmetry and Morse theory and am confused about the details of the instanton calculation which he uses to define a Morse complex (beginning at page 11 of the pdf) . ...
1
vote
2answers
68 views

Bloch theorem, Energy, Free electron

I'm trying to learn on my own a bit of solid physics to tackle semiconductors afterwards. I'm struggling with the Energy versus $k$ diagrams for a free electron which shows that for a single value of ...
1
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1answer
72 views

What is the significance of the difference in the eigenvalue equations of Bloch functions for electrons vs photons?

any text on photonic crystals will highlight the almost perfect analogy between electrons in a periodic potential and photons in a periodic dielectric. The analogies are: $$V(\vec r + \vec R) = ...
1
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1answer
54 views

Why are results of Bell's experiments considered to “break realism”?

Related to my previous question (Why would classical correlation in Bell's experiment be a linear function of angle?), as a newbie in quantum mechanics, I am also unable to find the reason to why ...
0
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3answers
125 views

Measurement of quantum state

Consider a particle in a box system.Assume its state to be a superposition of the ground and the first excited energy states.Consider two observers A and B (rest of the world).A made the measurement ...
2
votes
1answer
71 views

Is the resistance 0 in the ballistic regime?

Given that in the ballistic regime a particle (electron) can move freely without scattering (there are no impurities ), is the resistance through a ballistic sample zero?
1
vote
1answer
64 views
+50

Boundary Element Method or Boundary Integral Method Computational Aspects

I have to solve a Helmholtz equation inside a simply connected domain. I know that in general the boundary integral can be written as, $$\phi(x)=\int_V G(x,x') \rho(x')\ d^3x'+\int_S ...
0
votes
1answer
46 views

Geometric Interpretation of Rotated basis of Hamiltonian and collective Dicke states

Suppose I start with a basis of states for a two spin-1/2 particle system, namely, $\{\left|\uparrow\uparrow\right\rangle, \left|\downarrow\downarrow\right\rangle, ...
0
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1answer
49 views

Macroscopic Forces from QED

In QED the carrier for electromagnetic interaction is a photon, while macroscopic forces are due to electromagnetic interaction (by macroscopic forces I mean: normal force, object collision, friction ...
3
votes
2answers
39 views

Why would classical correlation in Bell's experiment be a linear function of angle?

Sorry if it's a newbie question, but I have trouble understanding the following part in the Wikipedia's explanation for the Bell's theorem: With the measurements oriented at intermediate angles ...
2
votes
1answer
76 views

Ground State Energy in Euclidean Spacetime

Calculating the transition amplitude in Euclidean spacetime is useful because from it we can extract the ground state energy and ground state wave-functions values. For example, let's assume we are ...
1
vote
2answers
89 views

Could the universe have evolved WITHOUT the non-determinism of quantum mechanics? [on hold]

(I'm going to make a few conjectures here - please answer the question in light of them as if they were true, even though of course they may be overly simplistic or wrong) Assuming that: the ...
0
votes
2answers
90 views

Does Free Will Theorem imply that quantum mechanics plays crucial role in our brain’s functioning (consciousness)?

Is opposite statement of Free Will Theorem right: If elementary particles have a certain amount of free will, then so must we? Because to me elementary particles does have a bit of free will – quantum ...
21
votes
4answers
2k views

Which is more fundamental, Fields or Particles?

I hope that I am using appropriate terminology. My confusion about quantum theory (beyond my obvious unfamiliarity with its terminology) is basically twofold: I lack an adequate understanding of ...
2
votes
2answers
43 views

Can we correctly define momentum operator only by means of position operator and their commutation relation?

In "J.M. Ziman. Electrons and Phonons: The Theory of Transport Phenomena in Solids" the author formally introduces the position (displacement) operator and then defines the momentum operator with the ...
-2
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0answers
33 views

Determine unknown potential & Hamiltonian in Schrödinger equation [on hold]

$x$ - time dependent Cartesian coordinate ; $m$ - time dependent mass of particle; Potential energy - unknown ! Hamiltonian - unknown ! Tasks: Make a formula to predict the $X(t$) ($x(t)$ for ...
2
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0answers
105 views

From Berry's phase to artificial Gauge potential

How a nonzero geometric phase in a loop is used to generate artificial gauge potentials? If possible, can you also tell how to generate the non-abelian artificial gauge potentials.
29
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8answers
11k views

Why don't electrons crash into the nuclei they “orbit”?

I'm having trouble understanding the simple "planetary" model of the atom that I'm being taught in my basic chemistry course. In particular, I can't see how a negatively charged electron can stay ...
19
votes
4answers
10k views

Why do electrons occupy the space around nuclei, and not collide with them?

We all learn in grade school that electrons are negatively-charged particles that inhabit the space around the nucleus of an atom, that protons are positively-charged and are embedded within the ...
0
votes
1answer
180 views

Integers, Energy levels, and wavenumbers for a particle in a 2D box

(This question is not about coding) I have built a little code in Python that allows the user to plot the energy vs the wave number of particle in a 2D box, depending on what values for the integers ...
4
votes
3answers
88 views

Complex Dirac field in antiparticle description

I understand that the Dirac equation has negative and positive sets of solutions and this contributes to its quantization by a superposition of two Fourier modes represented as creation and ...
0
votes
1answer
34 views

Will an electron gun fire behind it?

If an electron travels as a wave, can it therefore not be aimed with any precision? If you fire an electron gun, can't you aim it at a particular slit? If the electron travels as a wave, will an ...
0
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1answer
48 views

What is the cut-off for quantum superposition?

Is there an explanation as to how macro objects aren't in superposition? At what size do objects stop being in a state of superposition?
0
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2answers
50 views

Does yukawa potential of two particles have effect on each other?

Okay,a novice here.Suppose two particle interact with Higgs field.Does The Yukawa potential created by each of them affect each other or the interaction in any way.If so,what is it physical ...
2
votes
3answers
94 views

Proof for a time-ordering equation in Negele & Orland (1998)

Let $T$ be the time-ordering operator which orders operators $A_1(t_1), A_2(t_2), \ldots$ such that the time parameter decreases from left to right: $$T[A_1(t_1) A_2(t_2)] = A_2(t_2) A_1(t_1) \text{ ...
1
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1answer
28 views

Beam splitters for X-rays?

What is the lower bound for the wavelength concerning polarizing beam splitters? Especially I ask for interferometer experiments with single photons. Of course I know that they exist for all ...
2
votes
2answers
72 views

What is the performance of a silicon crystal that makes it an essential component to computing

I'm on a thread of interest in the precise physics that allow the creation of the computing process. It began as a question posted in search of an understandable explanation of what physical form ...
3
votes
0answers
36 views

Berry's phase: in which space does the degeneracy appear?

This question follows a previous one of mine: Adiabatic theorem and Berry phase. In his original paper [ M. V. Berry, Proc. R. Soc. Lond. A. Math. Phys. Sci. 392, 45 (1984) ], Berry discussed the ...
2
votes
1answer
29 views

Linearity of the time evolution operator for the reduced density matrix of an entangled state

Suppose to have a system $S$ immersed in an enviroment; the pure states are elements of $H_S \otimes H_E$, where $H_S$ is the hilbert space of the system and $H_E$ is the hilbert space of the ...
3
votes
3answers
270 views

How would a realist interpretation of the Mermin-Peres square look like?

How would a realist interpretation of the Mermin-Peres square with counterfactual definiteness and the existence of states prior to measurements look like?
2
votes
2answers
62 views

Differences between wave function and set of orthonormal wave functions?

I'm reading a QM book. It first says for wave function: "The state of a physical system (or particle) is completely specified by an entity associated with it called a wave function, Ψ , that in ...
1
vote
0answers
26 views

What is it that makes an electron maintain a distance from the positively charged nucleus? [duplicate]

What is it that makes an electron maintain a distance from the positively charged nucleus? Why aren't electrons merely pulled into and absorbed by the nucleus ?
1
vote
2answers
405 views

Bound state in a potential well?

Reading from http://quantummechanics.ucsd.edu/ph130a/130_notes/node151.html It says: This means that the solutions separate into even parity and odd parity states. We could have guessed this from ...
6
votes
3answers
644 views

Aharonov-Bohm Effect and Flux Quantization in superconductors

Why is the magnetic flux not quantized in a standard Aharonov-Bohm (infinite) solenoid setup, whereas in a superconductor setting, flux is quantized?
6
votes
1answer
359 views

Adiabatic theorem and Berry phase

As far as I can check, the adiabatic theorem in quantum mechanics can be proven exactly when there is no crossing between (pseudo-)time-evolved energy levels. To be a little bit more explicit, one ...
0
votes
2answers
129 views

Derivation of the Thermal Noise Spectrum

The thermal noise spectrum is given by: $$\mathcal{S}(f) = \frac{\hbar f}{2(e^{\frac{\hbar f}{kT}} - 1)}$$ This equation seems really similar to the Dirac-Fermi distribution but where does it come ...
3
votes
1answer
92 views

Local number operators in quantum field theory

Redhead claims in his paper "More ado about nothing" (http://link.springer.com/article/10.1007%2FBF02054660) that number operators associated with different space points (at fixed time) fail to ...
1
vote
1answer
87 views

details for the double slit experiment

In the double slit experiment with electrons, are all electrons going through the slits? If the electron gun is directed between two slits, than it should hit the central part between the slits, isn't ...
0
votes
1answer
32 views

Quantum mechanical proof of Conway's SPIN and TWIN axioms?

I think I understand correlations of EPR-state and GHZ-state which deal with spin-1/2 particles and (-1, 1) measured values. Conway's state is spin-1 particle state with (-1, 0, 1) measured values. ...
1
vote
1answer
54 views

Does this photograph portray double muon impact with nanogold atoms?

1PHOTO 1: Macro-photograph of an NIH/FDA TEM of a nanogold dark stained biological sample projected onto Silver Halide (AgX) photographic gel paper. On June 10 I questioned if PHOTO 1 ...
1
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2answers
79 views

Quantum Regime of Particles in Solids

On my midterm today, I read that when the deBroglie wavelength of a particle exceeds the spacing between the particles in a solid or liquid, the particles begin to behave quantum dynamically. Why is ...