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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2answers
618 views

Implementing simple atom model using density functional theory (DFT)

I am trying to write computer code which will find the energy and density function for an atom with $Z$ protons and $N$ electrons. I am working in 1D for simplicity and would like to make the overall ...
4
votes
1answer
186 views

What does the appearance of a classical particle fundamentally reduce to?

I've been reading an article that describes what seems to be a classical particle as a regularity in the global wavefunction over a quantum configuration space: When you actually see an electron ...
9
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3answers
2k views

A book on quantum mechanics supported by the high-level mathematics

I'm interested in quantum mechanics book that uses high level mathematics (not only the usual functional analysis and the theory of generalised functions but the theory of pseudodifferential operators ...
16
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6answers
163 views

Multiqubit state tomography by performing measurement in the same basis

For a $n$-qubit state $\rho$ we perform all projective measurement consisting of one-particle measurements in the same basis, that is, $$p_{i_1i_2\ldots i_n}(\theta,\varphi) = \text{Tr}\left \{ \rho ...
14
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1answer
159 views

Monte Carlo integration over space of quantum states

I am currently facing the problem of calculating integrals that take the general form $\int_{R} P(\sigma)d\sigma$ where $P(\sigma)$ is a probability density over the space of mixed quantum states, ...
2
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1answer
2k views

Feynman Path Integral Formula in Brian Cox' “A Night with the Stars” Lecture

The Youtube link keeps breaking, so here is a search on Youtube for Brian Cox' A Night with the Stars lecture. Pause the video on 40.32minutes. What you see he said is called Feynman's Path Integral. ...
4
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1answer
1k views

General procedure for Clebsch-Gordan expansions

I'm wondering if the Clebsch-Gordan series generalize to any orthonormal set of basis functions? If so, how would one go about deriving an expression for an arbitrary set of basis functions (perhaps ...
1
vote
1answer
504 views

Common Variables in Quantum Mechanics

I am an eighth grader (please remember this!!!) in need of some guidance in my school project on Quantum Mechanics, Theory, and Logic. I am attempting the create a graph of the Schrödinger Equation ...
3
votes
2answers
633 views

Is the free electron wavefunction stable?

The wavefunction of a free electrons is variously described as a plane wave or a wave packet. I am fairly happy with the wave packet, as it is localised. But if we change to the electron's rest ...
1
vote
1answer
140 views

Krauss operators for random unitary

Suppose I have a density matrix $\rho$ and I act on it with a unitary matrix that is chosen randomly, and with even probability, from $S = \{ H_1, H_2 \ldots H_N \}$. I want to write the operation on ...
4
votes
1answer
828 views

Relationship between nuclear spin and nuclear magnetic moment?

We know that nuclear magnetic moment can be expressed in terms of the expected value for nuclear spin as: $$\langle\mu\rangle =[g_lj+(g_s-g_l)\langle s_z\rangle]\frac{\mu_N}{\hbar}$$ (Cf. Krane), ...
6
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1answer
1k views

Degeneracy Pressure, What is it?

There has been numerous question, some violent even in physics@SE regarding PEP and EM forces. But what baffles me is what is degeneracy pressure? I know there are 4 fundamental forces- EM, gravity, ...
4
votes
1answer
248 views

Transpose Map Positive, But Not Completely Positive?

I am reading Introduction to Quantum Computing by Kaye, Laflamme, and Mosca. Here is a question I am struggling with: Exercise 3.5.6: Prove that the transpose map, which maps $\rho \mapsto ...
12
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1answer
617 views

Entanglement in time

Quantum entanglement links particles through time, according to this study that received some publicity last year: New Type Of Entanglement Allows 'Teleportation in Time,' Say Physicists at The ...
0
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0answers
38 views

Is the universe a quantum computer - is light speed barrier a computational constraint [duplicate]

Possible Duplicate: Is the universe a quantum computer - is light speed barrier a computational constraint Cross-posting this question, since physics.stackexchange has not provided any ...
1
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1answer
219 views

Entanglement and conservation

Is the following assertion sufficiently unique to merit a paper? Every absolute conservation law implies a corresponding form of entanglement, not just spin (angular momentum). Linear momentum ...
5
votes
2answers
142 views

Quantum entanglement of spin along multiple orthogonal axes

Picture an entangled pair of spin 1/2-spin particles with total spin 0. In the diagram, particle 1 of the pair is moving to the left (-y), and particle 2 to the right (+y). If a z-oriented SG$^*$ is ...
4
votes
4answers
502 views

Why does optical pumping of Rubidium require presence of magnetic field?

The optical pumping experiment of Rubidium requires the presence of magnetic field, but I don't understand why. The basic principle of pumping is that the selection rule forbids transition from ...
18
votes
3answers
2k views

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 ...
3
votes
2answers
763 views

Connections between classical and quantum mechanics?

I've done basic or introductory mechanics at the level of Resnick and Halliday. I'm currently studying calculus of variations and the Lagrangian formulation of mechanics on my own. I read somewhere ...
2
votes
2answers
200 views

Is there an overlap between quantum dynamics and math of brownian motion?

Suppose you have dynamics of a coherent state. The state presents a normal distribution of finding the particle. Does anyone know of any attempts to connect modern advances in the probability theory ...
5
votes
2answers
143 views

Is ground energy of interacting fermions always higher that that of bosons?

Consider two systems, each made of $N$ particles. In both systems particles interact pairwise and the interaction is given by the same Hamiltonian for both systems. Any other constraints and/or ...
8
votes
3answers
338 views

Does no-cloning theorem implies a no-comparison theorem?

I was reading about no cloning theorem and it arose a thought experiment, if there were a way of compare quantum states (for being equal) then you could build a pseudocloning machine that searches for ...
2
votes
2answers
167 views

Hamiltonian of a water molecule bounded to a surface

Where can I find a way to construct the hamiltonian of a water molecule bounded to a surface? More generally,how can one write the hamiltonian of an atom bounded to a surface?
4
votes
2answers
497 views

Neutron electric dipole moment and $T$ symmetry violation

Our textbook (and other sources I have found) says that non-zero electric dipole moment of neutron would violate $T$ symmetry. They prove this statement by first assuming ...
6
votes
2answers
1k views

How is information related to energy in physics?

I recently attended a talk by Dr. Ravi Gomatam on 'quantum reality', where the speaker suggested, that conservation of energy is not a fundamental law, and is conditional, but the conservation of ...
8
votes
2answers
719 views

Deriving Planck's radiation law from microscopic considerations?

In the usual derivation of Planck's radiation law, the energies or frequencies $\omega$ of the oscillators depend on the measurements $L$ of the black body. The model is such that the only ...
3
votes
4answers
328 views

Are there more bosons or fermions in the universe?

The question is in the title: are there more bosons or fermions in the universe? Or is there the same number of bosons and fermions? I think there is the same number but I don't know why exactly.
5
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3answers
282 views

What is the Quantum equivalent of chaos on a classical system? (if there's any)

This is a question that bugging me around for some time now. It is not clear to me what is the meaning of a chaos if we consider a quantum system. What is the mathematical formalism (or the quantum ...
2
votes
2answers
83 views

Another question about Shankar's notation

I have another question on the notation in Shankar. I think it's sloppy, but I also may just be misunderstanding it. Again, this is at the very beginning of the math intro. He has: $$a\left| V ...
3
votes
2answers
447 views

At what angle does a single atom “reflect” a single photon?

Does this question make sense in the quantum world? Imagining a single photon (wave packet?) interacting with a single atom (its electrons etc) how do we currently describe/define the emitted photon ...
2
votes
4answers
281 views

How can new interpretations of QM help?

There is some current work on interpretations of quantum mechanics. How do you think can interesting results in that area help physics? Can it change quantum physics or make it easier? Which ...
1
vote
1answer
278 views

Conserved quantum observables from symmetries *with density matrix*

I’ve read Ballentine where he derives the conserved observable operators (momentum, energy, ...) from symmetries of space-time. Can I read up such a derivation in more detail somewhere else or even ...
2
votes
0answers
78 views

Factorization of fermionic scattering integral in 2d momentum rep

the scattering integrals for fermions involves both momentum ($k$) and energy ($k^2$) conservation and a nonlinear phase space factor of a distribution function $f(k)$. $$\begin{multline}I(k) = ...
1
vote
2answers
263 views

Question on notation in Shankar's Quantum Mechanics - math intro on vector spaces

I'm just beginning Shankar's 2nd edition Quantum Mechanics and having some trouble with notation. He defines his vectors as "$\left|V\right>$" . And with a scalar multiplier as "$a\left|V\right>$" . ...
4
votes
1answer
62 views

Tip of a spreading wave-packet: asymptotics beyond all orders of a saddle point expansion

This is a technical question coming from mapping of an unrelated problem onto dynamics of a non-relativistic massive particle in 1+1 dimensions. This issue is with asymptotics dominated by a term ...
5
votes
2answers
2k views

Why are scattering matrices unitary?

In Griffith's QM book, he introduces scattering matrices as an end-of-the-chapter problem. For a Dirac-Delta potential $V(x) = \alpha \delta (x - x_0)$, I've derived the scattering matrix and ...
0
votes
1answer
973 views

Derivation of angular momentum commutator relations

I'm trying to understand the derivation of the angular momentum commutator relations. How is $$[zp_y, zp_x] ~=~ 0?$$ How is $$[yp_z, zp_x] ~=~ y[p_z, z]p_x?$$
1
vote
1answer
179 views

Quantum Cryptography

First question was a little bit ambiguous. Photons are passed through a linear polarizer that is oriented $\theta$ degrees again the photon passes through another linear polarizer that also have a ...
20
votes
5answers
3k views

Why not using Lagrangian, instead of Hamiltonian, in non relativistic QM?

When we studied classical mechanics on the undergraduate level, on the level of Taylor, we covered Hamiltonian as well as Lagrangian mechanics. Now when we studied QM, on the level of Griffiths, we ...
1
vote
1answer
162 views

Educational game [closed]

I am in the process of conceptualizing an iOS or computer game (a modification of Tetris) that would be suitable for motivated high school students and university undergraduates. It is meant to be an ...
6
votes
3answers
1k views

Electrons - What is Waving?

If an electron is a wave, what is waving? So many answers on the internet say "the probability that a particle will be at a particular location"... so... the electron is a physical manifestation of ...
1
vote
4answers
173 views

Is a macroscopic pair where I observe one of them quantum entanglement?

Of what little I know/understand about quantum entanglement can somebody confirm if the following experiment is a good analogy to quantum entanglement of pair of particles? PS: please don't laugh as ...
-2
votes
1answer
360 views

A quanta of time

A question of Quantum Time: Does a minimum interval of time cause wave-like behavior? If we think about the uncertainty principle, could it derive from a quanta of time? Does plank’s constant somehow ...
8
votes
7answers
682 views

How does such strange microscopic behavior at the atomic level (quantum mechanics) lead to the macroscopic behavior at our level?

So, I'm only a high school student researching quantum physics, and I find it very interesting. However, there's one question that keeps nagging at me in the back of my head. How exactly do odd ...
2
votes
1answer
613 views

Weinberg's way of deriving Lie algebra related to a Lie group

I was reading the second chapter of the first volume of Weinberg's books on QFT. I am quite confused by the way he derives the Lie algebra of a connected Lie group. He starts with a connected Lie ...
11
votes
4answers
824 views

Energy Measurements in a Two Fermion Double Well System

This question is related but my question here is much more elementary than discussions of the Pauli principle across the universe. There has been a fair amount of discussion around at the moment on ...
2
votes
3answers
338 views

Are electrons in different energy levels considered identical?

In QM we require that the state that describes the system, an atom say, be symmetric or antisymmetric under permuting the identical particles. What identical particles are we talking about here, all ...
3
votes
1answer
888 views

Angular momentum coupling-calculation of Clebsch–Gordan coefficients

I am facing problem in calculating the value of given Clebsch–Gordan coefficients representing the coupled angular momenta of two-particle system. For example $$\begin{pmatrix}2 & 1 & 2 \\ 1 ...
6
votes
4answers
361 views

Can an Electromagnetic Gauge Transformation be Imaginary?

The Hamiltonian of a non-relativistic charged particle in a magnetic field is $$\hat{H}~=~\frac{1}{2m} \left[\frac{\hbar}{i}\vec\nabla - \frac{q}{c}\vec A\right]^2$$. Under a gauge transformation ...