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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1answer
65 views

The momentum of a hole

I'm currently working through "A Guide to Feynman Diagrams in the Many-Body Problem" by R.D. Mattuck (self study, not a homework problem) and am stumped by the following problem: "In a system of free ...
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2answers
87 views

Can we describe mathematics using filters and matrices?

Can quantum mechanics be partly explained in terms of mathematical filters? Is there a way to explain some of it with matrices on an amateur level?
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0answers
23 views

Energy in an electromagnetic wave

A radio antenna creates EM waves through switching the polarization in the antenna at a certain frequency. I assume the the energy of the photons produced in this process amount to E=hf for each ...
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0answers
13 views

Entropy of Reeh-Schlieder correlations

Any state analytic in energy (which includes most physical states since they have bounded energy) contains non-local correlations described by the Reeh-Schlieder theorem in AQFT. It is further shown ...
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0answers
53 views

Rewriting $\langle {\bf k} \vert E,l,m \rangle$ as $\langle {\bf k} \vert ~k,l,m \rangle$ Spherical Harmonics

From Sakurai eq. 6.4.21a we have that $$\langle {\bf k} \vert E,l,m \rangle=\frac{\hbar}{\sqrt{M k}}\delta\left(E-\frac{\hbar^2 k^2 }{2M}\right) Y_l^m({\bf\hat k}),$$ where $M$ is the mass of the ...
0
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1answer
64 views

Quantum Mechanics - Observable

If $O$ represents an operator corresponding to an observable why does the following equality hold? $$\langle f(x)\, |\, O g(x)\rangle = \langle g(x) \,|\, O f(x) \rangle$$ It is used on the last ...
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0answers
33 views

group and phase velocity of free particle [duplicate]

If Schrödinger wave equation is for matter waves then for a free particle Group velocity $V_g =2$ Phase velocity $V_p$ But matter waves satisfy the relation $V_g V_p = C^2$ where $V_p>C$ Does this ...
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1answer
25 views

Band structure and band index

Please let me know If my understanding is right. For a given $\vec{k}$, $H$ is a function of $\vec{k}$ the energies vary discretely for $n$ ie.,the band index. For a given $n$, we choose all the ...
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0answers
27 views

Density of States of Free Particle in One Dimensions

I am using Quantum Mechanics by David H. McIntyre, chapter. This is problem 15.7: Find the density of states $g(E)$ for the case of a free particle in one dimension; further, show that the density of ...
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0answers
15 views

A problem concerning the calculation of parameters in a periodic system [on hold]

I am using Quantum Mechanics by David H. McIntyre, chapter 15. The question is 15.8: Find the single bound state energy of an electron in an isolated well of depth $V_{0} = 1$ eV and with width $b = ...
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0answers
17 views

What are the New Researches in the field of laser physics? [on hold]

I want to know the newest updates of science in the laser physics researches specially the theoretical part of it.
10
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1answer
128 views

Can nowadays spin be described using path integrals?

In Feynmans book, "Quantum mechanics and Path Integrals" he writes in the conclusions (chapter 12-10) With regards to quantum mechanics, path integrals suffer most grievously from a serious ...
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0answers
72 views

$\psi^*$ if you have sine or cosine function [on hold]

If my $\psi$ function is $\sin(\pi x/L)$. What is $\psi^*$ going to be?
2
votes
0answers
62 views

Different hamiltonians for quantum harmonic oscillator?

The Hamiltonian for a classical simple harmonic oscillator is $$ H = \frac{p^2}{2m} + \frac{1}{2}m\omega^2x^2$$ With the usual choice of the ladder operators $$a = ...
2
votes
1answer
84 views

What kind of problem in quantum mechanics can have an algebraic method of solution?

For example, a harmonic oscillator can have an algebraic solution, and hydrogen potential can also have an algebraic solution. Here the algebraic method of solution means that we can use the similar ...
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1answer
45 views

First Order Correction to wave function in ground state

I am looking at a spin 1/2 particle in a magnetic field. This has Hamiltonian $$H=-\mu s\cdot B_0$$ For simplicity, assume $B_0=B_0\hat z$ so $H=-\mu B_0$. I then apply a perturbative magnetic field ...
0
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1answer
38 views

Perturbation of coupled spin

I am given a system with Hamiltonian (all 1/2 spins) $$H_0=\alpha(S_1\cdot S_2)$$ I broke it down and found that there were four eigenstates: $|1,[0,\pm1]\rangle$ and $|0,0\rangle$. Each has an ...
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0answers
42 views

Non-commuting vector multiplication in GR

If the tensors of GR were composed of non-commuting vector multiplications, this would at least in spirit bring GR closer to QM. Has this approach been attempted?
3
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1answer
51 views

Is obtaining the coordinate representation of momentum operator from commutator more fundamental than generator of translation

Related post: What is the most general expression for the coordinate representation of momentum operator? There are two methods of obtaining the coordinate representation of momentum in quantum ...
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0answers
26 views

Proving two forms of atom-field interaction perturbation Hamiltonian are equivalent

In the presence of an electromagnetic field in the dipole-approximation (${\boldsymbol A} = {\boldsymbol A}(0,t)$) we have the two forms $$H_{{\boldsymbol d}\cdot {\boldsymbol E}} = - q {\boldsymbol ...
4
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1answer
97 views

Time-Energy Uncertainty Principle and Operators

In most of examples, I notice that uncertainty principle for time & energy is given between mass & lifetime. The UP for time and energy is $$ \Delta t\,\Delta E\geq\frac h{4π} $$ where $$Δt ...
2
votes
2answers
161 views

From Quantum Mechanics to Classical Mechanics [duplicate]

Is it possible, and has it been attempted, to use quantum mechanics to deduce Newtonian, macroscopic level mechanics laws as was the case of statistical mechanics deriving thermodynamic relations?
2
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1answer
27 views

All angle dependence in $\mathrm{d}LIPS_2$?

Recall that $\mathrm{d}LIPS_2$ (one particle decaying into two particles of the same mass) is given by $$\mathrm{d}LIPS_2 = \frac{\vert{\bf k_1'}\vert}{16\pi^2\sqrt{s}}\mathrm{d}\Omega_{cm}.$$ In a ...
3
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0answers
81 views

Mandelstam variables 1 positive 2 negative

The three Mandelstam-variables are defined as: $$s=(p_A+p_B)^2=(p_C+p_D)^2,$$$$t=(p_A-p_C)^2=(p_B-p_D)^2$$$$u=(p_A-p_D)^2=(p_B-p_C)^2.$$ Where A and B are the incoming particles and C and D are the ...
2
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0answers
43 views

Log-interaction term calculation

I have a question regarding calculating the following integral with cutoff. $$ \int_{-\infty}^{\infty} \frac{d\omega}{|\omega|} \cos(\omega(\tau_i-\tau_j)-1)$$ How should I set up the correct cutoff ...
3
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1answer
59 views

De Broglie Wavelengths

I have a working knowledge of wave-particle duality, I think. I know the de Broglie wavelength is a sort of probability of finding a particle in a specific position, and is calculated by ...
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1answer
61 views

Normalized Projection Operator

What is meant by normalized projection operator? What is its physical meaning in quantum mechanics? I am pretty confused regarding the physical interpretation of both projection operator and ...
3
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0answers
58 views

Naive questions on the ground states of Kitaev model

Up to now, I found myself still does not have a deep understanding of the honeycomb Kitaev model, and I got some naive questions about the ground states (GSs) of the this model (with open boundary ...
0
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1answer
27 views

Expectation value of Hamiltonian on number state [on hold]

Hamiltonian is defined by $H_I = \hbar \omega (\hat{a}^+ \hat{a} + 1/2)$ What is the expectation value of the energy on the number state $$\vert \psi \rangle = \frac{1}{\sqrt{2}} ( \vert 1 \rangle ...
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1answer
41 views

Interpretation of Heisenberg's uncertainty principle

Heisenberg's uncertainty principle is one of the most fundamental principles on which quantum mechanics is based on. But it is also one of the most confusing laws we encounter. My doubt is whether the ...
0
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2answers
48 views

Measurement of Mass and Momentum of a particle simultaneously

In quantum mechanics can the mass and the linear momentum of a particle be measured precisely or do they commute ?
0
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1answer
62 views

How to derive the commutation relationship between $\hat{L}^2$ and $\hat{\textbf{p}}$ [on hold]

How to prove that $$[\hat{L}^2,\hat{\textbf{p}}] = i\hbar(\hat{\textbf{p}}\times\hat{\textbf{L}} - \hat{\textbf{L}} \times \hat{\textbf{p}})$$ I tried to expand $\hat{L}^2$: ...
0
votes
1answer
29 views

Electronic configuration for singlet and triplet states

Is there a difference in the electronic configuration for singlet and triplet states? For example, He atom has 1s2 configuration in its ground state (singlet state) But what about when the He atom is ...
0
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0answers
23 views

Quantum Cryptography Open Problems [on hold]

I am a 3rd year Physics undergraduate interested in Quantum Cryptography. This summer , I want to work on a open problem in Quantum Cryptography. I have credited courses such as Quantum Computation ...
7
votes
2answers
167 views

Lie algebra and Lie group about quantum harmonic oscillator

We know that in the quantum harmonic oscillator $H=a^\dagger a$, $a^\dagger$, $a$, $1$ will span a Lie algebra, where $a, a^\dagger$ are the annihilation and creation operators, and $H$ is the ...
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1answer
43 views

Position and potential Energy

Why are the position and potential energy of a particle able to be measured precisely in Quantum Mechanics? I mean why do they commute with each other?
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0answers
33 views

How to evaluate the various PARITY?

In nuclear vibrations how do we get $0^+$ $2^+$ $4^+$... excite states for nuclear collective model ? I meant, I am searching for a method that will provide me the different parity and the states. ...
0
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1answer
52 views

Collapse of the Free Particle Wave Function

The time evolution of the one-dimensional quantum mechanical free particle ($V(x) = 0$ $\forall x$) is described by the following Schroedinger equation $ -\frac{\hbar^2}{2m}\frac{\partial^2 ...
0
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1answer
32 views

Radiaton of black body [on hold]

We have : $E=h/f$ I realised that the problem what quanta solved was that $h/0$ equals infinity but energy can't be infinity. But when frequency is zero we haven't any energy to calculate - there is ...
0
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1answer
43 views

Symmetric, antisymmetric and mixed symmetry particles

Can someone explain to me the concept of symmetric, antisymmetric, and mixed symmetry when talking about the states of identical particles?
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0answers
22 views

Help with 1D and 2D density of states

I am currently looking at changes in DOS when sampling recipocal space finely. More precisely, I am looking at the expressions $$\rho_\text{1D}(E)\text{d}E = \frac{m}{\pi \hbar} \sum_i ...
0
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0answers
16 views

Grover search algorithm for more than one marked elements [on hold]

Grover search algorithm is a powerful tool for unstructured database search purposes. The two operations (Phase inversion and Inversion about the mean ) join hands to give the marked needle. I was ...
0
votes
1answer
60 views

Is $\langle k \vert k_1k_2\rangle=0$

Using that $$ \vert k_1k_2\rangle = a^\dagger({\bf k_1})a^\dagger({\bf k_2})\vert 0 \rangle$$ and the commutation relations $$[a({\bf k}),a^\dagger({\bf k'})]=(2\pi)^32\omega\delta^3(\bf {k}- \bf ...
1
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1answer
56 views

Normalizing continuous eigenstates

As far as I understand, to normalize the eigenfunctions, corresponding to the continuous spectrum, we use Dirac delta function: $\langle \psi_\lambda \mid \psi_{\lambda'} \rangle = \delta(\lambda - ...
1
vote
1answer
59 views

Multiparticle generalization of $\langle \vec k \vert E,l,m \rangle$ spherical harmonics.

From Sakurai eq. 6.4.21a we have that $$\langle {\bf k} \vert E,l,m \rangle=\frac{\hbar}{\sqrt{M k}}\delta\left(E-\frac{\hbar^2 k^2 }{2M}\right) Y_l^m({\bf\hat k}),$$ where $M$ is the mass of the ...
0
votes
1answer
38 views

Normalization of $\langle p_1 p_2 \vert p\rangle$ in RelQM and NonRelQM

Suppose a particle p of three momentum $\vec p$ decays into two particles of 3-momentum $\vec p_1$ and $\vec p_2$. I know the question might sound stupid but right now my brain is full stop: Is the ...
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1answer
39 views

Determination of entangled states

The definition of an entangled state $|\Psi\rangle$ is that it CANNOT be factored into $$|\Psi\rangle=|\psi\rangle_1\otimes|\phi\rangle_2$$ I am kind of confused on what is meant by a quantum ...
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3answers
169 views

Why is $|\Psi|^2$ the probability density?

I am starting with Quantum Mechanics, learning online. I can't seem to find the reason for $|\Psi|^2$ being the probability density of finding an electron. They've just taken it for granted ...
0
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1answer
33 views

Uncertainty Principle Upper-bound?

In quantum mechanics, is there an upper bound for the uncertainty principle? I know that quantum harmonic oscillator (QHO) has the uncertainty relation $\sigma_x\sigma_p = \hbar(n+1/2)$, but I think ...
0
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1answer
36 views

Second quantization of the energy current operator

I am reading Mahan many-particle physics(3rd edition). On P25 he derive the energy current operator in second quantization like this: Equation of energy conservation: $$\frac{\partial ...