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
98 views

What are correlated magnetic moments?

My book has the following sentence and I don't understand what correlation or lack of correlation means: At high temperature the magnetic moments of adjacent atoms are uncorrelated (to maximize ...
4
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1answer
99 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 ...
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3answers
237 views
+100

Does Quantum Mechanics Allow Macroscopic Anomalies?

I've read a few other posts, and none seem to give me an answer that satisfies my curiosity. Thus far I've only been studying time independent QM, so I'm not even sure how wave functions evolve over ...
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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
44 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?
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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 ...
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2answers
164 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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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
66 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 ...
9
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1answer
241 views

Nuclear Magnetic Resonance (NMR) Conceptual Questions

Let $M$ be the magnetic moment of a system. Below are the Bloch equations, including the relaxation terms. $$\frac{\partial M_x}{\partial t}=({\bf M} \times \gamma {\bf H_0})_x-\frac{M_x}{T_2} $$ ...
15
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5answers
381 views

direct sum of anyons?

In the topological phase of a fractional quantum Hall fluid, the excitations of the ground state (quasiparticles) are anyons, at least conjecturally. There is then supposed to be a braided fusion ...
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1answer
27 views

Expectation value of Hamiltonian on number state [closed]

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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2answers
52 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 ?
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1answer
64 views

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

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
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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 ...
1
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1answer
97 views

Quantum Philosophy a la John Bell

I recently discovered this website http://www.quantumphil.org/ and wondering whether Quantum Philosophy is an actual field, or just an aspect of QM? Apologies if this is in the wrong place.
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2answers
105 views

What is the reason behind why a quantum particle cannot be at rest?

So I've seen different reasonings for this; which is correct, or are they both corollaries of each other? 1) For a particle to be at rest, we would know its momentum and therefore by Heisenberg's ...
6
votes
2answers
230 views

How does the proof of operator commutativity work with non-continuous operators?

In some books, a proof that if two self-adjoint operators $A$ and $B$ share a common eigenbasis $\{\phi_n\}$, then they commute is given as follows : For any $\phi_n$, $$AB\ \phi_n = a_n\ ...
0
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1answer
31 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 ...
3
votes
3answers
115 views

Advantage of taking qutrits in place of qubits

In general, all the quantum algorithms which I have read so far use qubits (so the space is $\mathbb{C}^2$) and the tensor products of the qubit spaces (space is ${\mathbb{C}^2}^{\otimes n}$). So my ...
0
votes
2answers
336 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 ...
0
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0answers
26 views

Quantum Cryptography Open Problems [closed]

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 ...
1
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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
votes
1answer
215 views

Coordinate system

Quoting from 'Nuclear Physics - Theory and Experiment' by RR Roy, BP Nigam 2005 edition Link to text How did the author arrive at equations (23a, 23b,23c)? Chapter 8 Nuclear model II, 8.7 ...
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1answer
32 views

Radiaton of black body [closed]

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
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 ...
2
votes
1answer
195 views

Given wave function at $t=0$, what is the process of deriving time dependent wave equation?

Suppose $$\Psi (x, t=0)=Ae^{i\alpha _1}\psi _1(x)+Be^{i\alpha _2}\psi_2(x)+Ce^{i\alpha _3}\psi_3(x).$$ If $\psi _n$ are the energy eigenfunctions how would I derive $\Psi (x,t)$? I am having trouble ...
0
votes
1answer
143 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 ...
0
votes
1answer
39 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 ...
0
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1answer
44 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?
0
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1answer
109 views

Electron Decay, Why are there P and higher orbitals?

Related: Decay from excited state to ground state My confusion arose initially from the definition of binding energy being the lowest energy state (n=1) in the hydrogen atom. This, I assume, is ...
1
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0answers
23 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 [closed]

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
2answers
84 views

Calculating states of entangled and disentangled qubits

I'm writing a quantum computer simulator (about 8 qubits) and I know most of the basics (i.e. how to calculate the effect of a quantum gate on a qubit). But I have hit a wall. Is it possible, with ...
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 ...
3
votes
1answer
77 views

Time-orded operator in Srednicki

On page 51 Srednicki states, "Note that the operators are in time order...we can insert $T$ without changing anything". This I agree with. But then on the next paragraph he states "The time order ...
1
vote
1answer
60 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
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1answer
32 views

Single-channel vs multi-channel scattering

I am studying quantum scattering and stumbled upon the "scattering channel" and "single- and multi-channel scattering" terms. However, I didn't manage to find any sufficiently formal definitions of ...
2
votes
0answers
95 views

How to understand the transmission coefficient from the following question?

I want to understand the transmission coefficient and construct a time-independent Schrodinger equation where $$ V(x)=\left\{ \begin{array}{c c} \delta(x), & |x| < 1 \\ + \infty, & ...
3
votes
1answer
512 views

Transmission and reflection

What is the transmission amplitude of a wavefunction $\phi(x)=e^{ikx}(\tanh x -ik)$? I would have thought that it is $\tanh x -ik$ since this is the factor associated with the forward travelling ...
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 ...
9
votes
5answers
349 views

What happens when we bring an electron and a proton together?

I have a couple of conceptual questions that I have always been asking myself. Suppose we have an electron and a proton at very large distance apart, with nothing in their way. They would feel each ...
1
vote
1answer
145 views

Shouldn't Quantum Mechanics change in a black hole?

I recently learnt that the conservation laws are a consequence of the symmetries of space and time (the Lagrangian in Newton mechanics). Since space-time change in a black hole wouldn't quantum ...
1
vote
1answer
57 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 - ...
0
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3answers
172 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 ...
1
vote
1answer
41 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 ...
3
votes
2answers
173 views

Composition of squeeze operators?

I'm wondering if it exists a composition law for the squeezing operation ? I guess so for geometric reason, since they are (generalized, and the phase is annoying of course) hyperbolic rotations of ...
0
votes
1answer
386 views

Stark effect in two level atomic, laser-driven system?

In a two level atomic system (Rabi oscillating problem) the perturbative potential is oscillating / sinusoidal because it comes from the electric field from the laser. Now stark effect is the ...