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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9 views

Tensors of rotations about an arbitrary vector in C^2

I'm trying to solve the following equation: $$e^{-i\theta/2 \sigma_{\vec{i}}^A} \otimes e^{-i\theta/2 \sigma_{\vec{i}}^B} |\Psi\rangle_{AB} = e^{i\phi} |\Psi\rangle_{AB} $$ where $e^{i\phi}$ should ...
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0answers
19 views

System without ground state is not real in nature?

We know that Coulomb force is real phenomena in nature and with Coulomb potential $V(x) \thicksim -\frac{1}{|x|}$ lowest energy is bounded in hydrogen atom. But it's mathematically clear that if ...
2
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1answer
62 views

Interpretation of $\vec{x}$ in QFT

I am still at an early stage of studying Quantum Field Theory (I am reading QFT In A Nutshell by A. Zee). In the book I'm reading, it starts from a discrete lattice of material "lumps" labeled by ...
4
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0answers
39 views

Density matrix formalism and group representation

The postulates of quantum theory can be given in the density matrix formalism. States correspond to positive trace class operators with trace 1 on a Hilbert space $\mathcal{H}$. Composition is defined ...
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1answer
105 views

Complex Quantum Wave [on hold]

Can the complex nature of quantum wave arise from the fact that particle is represented as wave packet in spatial frequency and particle's total energy is represented as wave packet in time frequency? ...
2
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1answer
74 views

How does Dirac form this conjugate imaginary equation?

On page 30 of Dirac's book $$\xi|P\rangle = a|P\rangle\tag{12}$$ He then says Suppose we have a solution of (12) and we form the conjugate imaginary equation, which will read $$\langle ...
3
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1answer
35 views

What is relationship between Quantum tunnelling and Gravitational potential energy of stars?

Are there a direct mathematical relationship between Quantum tunnelling and Gravitational potential energy of stars? The true source of the Sun's energy was shown by Hans Bethe to be nuclear fusion ...
3
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2answers
35 views

Observing a particle over a certain domain

I was just thinking: in Quantum Mechanics, we start out with that whole collapsing business by observing the x position of a particle. I was thinking: why do we have to do that? What if we only ...
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1answer
42 views

Degeneracy in One Dimension

I'm reading this wikipedia article and I'm trying to understand the proof under "Degeneracy in One Dimension". Here's what it says: Considering a one-dimensional quantum system in a potential ...
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2answers
87 views

How do photons “decide”?

I was reading that when horizontally polarized light hits a vertical Polaroid all the light is blocked out. But when the Polaroid is off the vertical, some but not all photons "decide" to jump into ...
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0answers
33 views

How to carry out the perturbation expansion of an anharmonic oscillator to high orders?

I think this is a standard problem in quantum mechanics. Consider the anharmonic oscillator $E \psi = \left(- \frac{1}{2} \frac{\partial^2}{\partial^2 x } + \frac{1}{2}x^2 + \epsilon x^4 \right) ...
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0answers
37 views

Can be this configuration used to faster than light communication?

I know from some popular science articles or books that is possible to make special pairs of particles which are quantum entangled. Then each of entangled particles can be moved to different places ...
3
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27 views

Reduce density matrix for given eigenfunction [on hold]

My question is about how to find reduce density matrix for partition of given eigenfunction. Full question is just in image.
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1answer
44 views

Expectation value of number operator $\hat{n}$

I'm studying for my quantum mechanics test and I've stumbled on this problem. They want the expectation value of $\hat{n}$, $\langle \hat{n} \rangle$, with this given $\psi$ at $t=0$: $$ \lvert ...
3
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2answers
166 views

Measuring non-commuting observable at once

Given an Hilbert space $H$ (finite dimensional for sake of clarity), and two non-commuting operators $$A = \sum_a a |a\rangle\langle a|$$ and $$B=\sum_a b |b\rangle\langle b|,$$ is it possible to find ...
3
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2answers
127 views

Infinitely many degeneracy of Landau level: Countable or Uncountable?

Description of Landau levels can be found in many standard textbooks of quantum mechanics and here. Two ubiquitous solutions apply either the symmetric gauge $\vec{A}=(-\frac{1}{2}By,\frac{1}{2}Bx,0)$ ...
3
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0answers
27 views

Rabi oscillations with quantized light: which is the “quantum” effect, collapse, revival or both?

In wikipedia http://en.wikipedia.org/wiki/Jaynes%E2%80%93Cummings_model#History it is stated that It was later discovered that the revival of the atomic population inversion after its collapse is ...
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2answers
178 views

On deriving Schrodinger Equation

I do know that one can't actually derive any axiom, but here is my serious attempt to explain Time Independent Schrodinger Equation with minimum preliminary knowledge. In the following $f$ is ...
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0answers
66 views

Why is graphene the only (stable) 2D sheet structure? [duplicate]

I know that Carbon molecules can form different structures depending on how they bond with each other: graphite, diamond, graphene and fullerene. As far as I understand, graphene is just a "sheet" of ...
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1answer
57 views

Scattering theory textbooks

I am looking for a possibly extensive list of great textbooks on elastic and inelastic scattering of particles within quantum field theory. So far I am familiar with: Peskin and Schroeder: An ...
0
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1answer
59 views

Commutativity of Position Operators

Does the position operator $q_{i}$ of one harmonic oscillator commute with the position operator $q_{j}$ of another different harmonic oscillator? In other words, is $q_{i} q_{j} = q_{j} q_{i}$ true? ...
1
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1answer
77 views

Time evolution of a quantum system

A quantum system has Hamiltonian $H$ with normalised eigenstates $\psi_n$ and corresponding energies $E_n$ ($n = 1,2,3...$). A linear operator $Q$ is defined by its action on these states: $$ ...
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0answers
22 views

Require Help for Graphene Based experiments [on hold]

I really need a software that can help me with graphene based experiments. Is there a software which could allow me to run all types of simulations for graphene layers focusing on photovoltaic cells? ...
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0answers
32 views

Momentum of electron problem [duplicate]

Recently, my friend bemused me with a question related to the momentum of an electron. The confusing logic is stated below: Since an electron is a particle and according to classical physics, we know ...
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0answers
84 views

General wave packet in Schrödinger equation?

Can I state general wave packet in arbitrary potential $V(x)$ in the following form? $$\psi(x,t) = \frac{1}{\sqrt{2\pi \hbar}} \int \hat{\psi}(p,t) e^{ipx/\hbar}dp=\frac{1}{\sqrt{2\pi \hbar}}\int ...
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41 views

How to make scattering matrix? [on hold]

I need to make a scattering matrix. Potential is unknown. I have the list of scattering data: time, mass and coordinate of the particle. How to make scattering matrix by the given data?
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3answers
125 views

Can a bullet really fly through space forever?

Some people says that if it would be possible to shoot a bullet so high that it would get over the Earth gravitational pull, the bullet could fly through space forever, because of no deceleration of ...
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0answers
18 views

How is it shown that the composition of two real operators is generally not real? [duplicate]

Dirac on page 28 of his QM book writes: Thus the conjugate complex of the product of two linear operators equals the product of the conjugate complexes of the factors in the reverse order. As ...
3
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0answers
35 views

Entanglement g-2-experiment - Which components do I need?

I would like to measure whether my source emits entangled photon pairs. To that order I want to build a g-2-experiment, which measures photon coincidence counts as a function of time delay between ...
0
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1answer
35 views

How to construct this oracle quantum gate?

I was reading the paper Quantum Computational Complexity in the Presence of Closed Timelike Curves. In this the author mentions that following quantum oracle gate which operates on $n+1$ qubits, can ...
0
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1answer
51 views

Does a normal torch emit entangled photons?

I was reading a sciencenews.org post about three photons being entangled. My question here is, why is the chance of producing an entangled pair once in a billion times? Isn't every particle produced ...
0
votes
1answer
42 views

Why a hole in the Dirac sea can be seen as having opposite energy?

In the Dirac's old attempt of relativistic quantum mechanics, a hole in the $E'$ level of the Dirac sea was interpreted as a particle of opposite charge and positive energy. I do get why it can be ...
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53 views
+100

What methods exist to calculate the density of states in the continuum of a molecule?

Say I have an arbitrary molecule in the Born-Oppenheimer approximation, and furthermore say that I can approximate the molecule as having only one active electron. What methods exist to calculate the ...
1
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1answer
45 views

How many wavefunctions are in a minimal basis set for benzene?

I am reading Modern Quantum Chemistry by Szabo and Ostlund and on page 62 he says "A minimal basis set for benzene consists of 72 spin orbitals." I tried to understand this number but failed. ...
0
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0answers
36 views

Quantum physics presentation topic [closed]

i am doing my advanced quantum mechanics course and the instructor want me to deliver a presentation end of the course.. The topics are: Born-Oppenheimer Approximation → Berry Phase Non-Hermitian ...
5
votes
3answers
248 views

Tensor product notation convention?

For two particle state, the Dirac ket is writren as $$\lvert\textbf{r}_1\rangle \otimes \lvert\textbf{r}_2 \rangle. $$ Then how do we write its bra vector, $$\langle\textbf{r}_1\rvert \otimes ...
1
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0answers
21 views

Does it matter in which order settings will be changed during CHSH-inequality check experiment?

Does it matter in which order detector settings will be changed when checking CHSH inequality? For example, i'm trying to build a simple (and very approximate) computer simulation of experiment. Now ...
2
votes
1answer
30 views

Does the relative angular momentum of the nucleons contribute to the spin of the nuclei?

Imagine we have a nucleus. We do talk about spins of nuclei. Is this spin the total angular momentum of the nucleus, that is, spins and relative angular momentum of all of the nucleons? If so, why? ...
2
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0answers
27 views

Spin via Change of Phase

Thinking of spin as arising from a change in the phase of a wave function: The angular momentum is defined by the change of the phase of the wave function under rotations, which may come from the ...
1
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2answers
209 views

Has magnetism been experimentally demonstrated at the quantum level?

I've learned that magnetic fields are generated by electric currents, and that electric current is the motion of electrons and stuff like that. Many textbooks also talk about "point charges" and have ...
4
votes
3answers
254 views

What does the Schrodinger Equation really mean?

I understand that the Schrodinger equation is actually a principle that cannot be proven. But can someone give a plausible foundation for it and give it some physical meaning/interpretation. I guess ...
2
votes
0answers
25 views

How does a photon travel through an electron cloud?

We all know that the exact position and exact velocity of an electron in an atom cannot be determined simultaneously, as per the Heisenberg uncertainty principle. We only talk about the probability of ...
0
votes
0answers
18 views

Quantized modes of EM field in a cubic cavity

I am trying to solve for Electric field modes in a cubic cavity with perfectly reflecting walls. I know that for the modes, I have the standard Helmholtz Equation $$(\nabla^2+k^2)E_i=0$$ And I want ...
0
votes
1answer
31 views

compressibility of cold atoms in optical lattices

The compressibility of cold bosons in an optical lattice is defined as $\kappa = \frac{\partial \langle n\rangle}{\partial \mu}$, where $\langle n\rangle$ is the density and $\mu$ is the chemical ...
1
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0answers
46 views

Imaginary Angular Momentum [closed]

I recently came across a problem online where it asks you to interpret an imaginary angular momentum about an axis. Apparently there's a chance it has to do with superconducting. What is the correct ...
2
votes
1answer
64 views

Quantum Harmonic Oscillator - Normalizability of Annihilated Ground State

The common line of deductions in the operator analysis of the quantum harmonic oscillator goes something like this: It is derived that the action of the annihilation operator $a$ on an eigenfunction ...
0
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1answer
48 views

Is there any defect in Rutherford's atomic model according to quantum theory?

According to quantum mechanics charged bodies do not emit energy. Then why the atomic model of Rutherford has the defects of collapsing nucleus, continues spectrum.
1
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0answers
29 views

quantum hall effect and hamiltonian [closed]

I need a good book or lecture on quantum hall effect. my supervisor wants me to find the Hamiltonian for the Qunatum hall effect, he want me to find this from this relation if it looks like a 2nd ...
2
votes
1answer
57 views

References on experimental realization of quantum one-dimensional infinite-well model

Can someone point me to the examples, or references, of experimental realization of the quantum one-dimensional infinite-well model? [EDIT] The motivation of this question is the curiosity - though ...
3
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0answers
49 views

Why does this condition ensure that the residue of the propagator is 1?

The corrected propagator is given by $$\Delta'(q)=\frac{1}{q^2+m^2-\Pi^*(q^2)-i\epsilon}$$ ($\Pi^*$ is the sum of all irreducible one-particle amplitudes) I get that the residue of the original ...