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
407 views

Probability current vs. direction of wave function

I did an exercise for my Quantum-Mechanics Lecture: Let $\hbar$=2m=1. A particle in 1 dimension has $j(x)=2\ Im(\overline{\psi} (x) \ \psi'(x))$ and it's to show that there are superpositions $\psi ...
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2answers
61 views

Unitary Confirmation

I am asked to show that an new defined operator: $$U_{\beta} = \exp(\displaystyle\frac{i\beta L_z}{\hbar})$$ is unitary, where $$L_z = -i\hbar\,\,(x\displaystyle\frac{\partial}{\partial y} - y ...
4
votes
3answers
909 views

Are matter waves transverse and can they be polarized?

Are matter waves transverse and can they be polarized? What I know:I'm aware of the de Broglie matter waves hypothesis and de Broglie wavelength relation(at a very basic level as part of high school ...
2
votes
0answers
128 views

Choice of X-ray scatterer in Compton effect

I am going to perform an experiment on Compton Scattering, and I am going to use an X-ray scatterer to scatter the incident X-rays. I have been instructed that Acrylic Glass slab are the best for this ...
5
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2answers
198 views

Do we need to expand the potential in a power series to show $[x, V(x)] = 0$?

Today in class (Intro to QM) we went over a couple of commutators. Among them was $[x, V]$, where $V=V(x)$ is a potential. What the teacher said to prove this is zero was: let's assume $V$ is analytic ...
2
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0answers
376 views

Theoretical or experimental violations of the 2nd Law of Thermodynamics? [closed]

Theoretical challenges to the 2nd Law? What are some the theoretical challenges to the 2nd Law? (cf. Čápek, Vladislav, and Daniel P. Sheehan. Challenges to the Second Law of Thermodynamics: Theory ...
1
vote
1answer
70 views

Simple photon recoil question

Imagine two charges A and B separated by some distance. Charge A emits a photon which is absorbed by charge B. Is the recoil momentum received by charge A always equal and opposite to the momentum ...
-1
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1answer
154 views

Do electrons have structure in quantum gravity?

I have read Luboš Motl's blog and he says in QG electrons must be composite and have structure because QG says there can be no point like particles and everything above the Planck size can be resolved ...
2
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0answers
135 views

How to calculate angular momentum per second for a photon beam? [closed]

Given a photon polarization state $$|\phi\rangle = \frac{3}{5}|x\rangle + \frac{4i}{5}|y\rangle,$$ a beam of photons transmit $N$ photons per second in such a state. An L-polarized photon has an ...
4
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2answers
609 views

Understanding the Wave Function and Excited States

A wave function is an infinite dimensional vector space, how can it "live" in $\mathbb{R}^3$? Given the equation that is built like: $$\Psi (x,t) = \sum ^{\infty} _{n=1} c_n \psi _n (x) e^{-i E_n t / ...
5
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1answer
2k views

Orthonormality of Radial Wave Function

Is the radial component $R_{n\ell}$ of the hydrogen wavefunction orthonormal? Doing out one of the integrals, I find that $$\int_0^{\infty} R_{10}R_{21}~r^2dr ~\neq~0$$ However, the link below says ...
1
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1answer
84 views

Simple QM question about Sy matrix

Given a spin 1/2 particle in state $|\alpha\rangle=\begin{bmatrix}a \\b\end{bmatrix}$, what is the probability of it being measured in the $S_{y+}$ state. Is this equivalent to, if $S_y$ is measured ...
2
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1answer
829 views

Wave function collapse

When we try to measure the position of a system, wavefunction collapses to form a spike. After a while, the wavefunction spreads again, and you take another measurement, the results will be different" ...
13
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1answer
516 views

Operator that describes particle detector

In non-relativistic QM, the position of a particle is an observable. In QFT, fields are the observables. However, particles must have some sort of position, otherwise we wouldn't see pictures like the ...
2
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2answers
115 views

Quantum uncertainty in cell functions

In class today (philosophy of the mind) we discussed the ideas of Richard Lewontin. He stated that in determining the phenotype of a gene we must take into account the environment but also quantum ...
1
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1answer
110 views

Weird Behaviour of the act of measurement to a quantum system

I and my friend were disputing about some weird behaviour of the act of measuring some observables quantities e.g. Energy, position. But I still don't think what he said is strictly true. He said" ...
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1answer
2k views

Writing a Wavefunction as a Linear Combination of Eigenstates

We have the following wavefunction for the hydrogen atom: $$\psi(r,\theta,\phi)=\frac{1}{\sqrt{4\pi}}\frac{1}{(2a)^{3/2}}\frac{r}{a}e^{-r/2a}\sin(\theta)\sin(\phi)$$ where $a$ is the Bohr radius. ...
2
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2answers
170 views

Angular momentum matrices (Schiff section 27)

On page 203 3rd edition of Schiff we are given the angular momentum matrices ${J}$ for $j=1$. I am curious as to how these relate to orbital angular momentum for $j = 1$. If we take the corresponding ...
4
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2answers
563 views

How much time does it takes an electron to tunnel through a barrier?

I know that in quantum mechanics there is no "time operator", so such a question is ill-posed. Anyway if the tunneling is instantaneous, this would imply an information transmission faster than $c$. ...
2
votes
1answer
70 views

Purposes of QEC stabilizers

I am going through the idea of stabilizer formalism. Defined what is a Pauli group $P_n$ and its properties, we describe a stabilizer set $S$ as: $$S\subset P_n$$ The stabilizer set establishes ...
2
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0answers
91 views

Ehrenfest's theorem on Gaussians

Considering the free evolution of a Gaussian wave packet, is it possible to use Ehrenfest's theorem to determine the average value of momentum given that of position? And I imply the simplified ...
4
votes
1answer
212 views

Correct way to do a Thomas-Fermi approximation for cold gases

I have calculated the total Gross-Pitaevskii energy for a 2D Bose-Einstein condensate in an harmonical trap, using a variational gaussian wave function with a variational parameter b. Now I want to ...
1
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2answers
1k views

What is the significance of electron spin quantum number?

Somewhere I read that spin quantum number is a particularly interesting theory of quantum mechanics as what it really implies is that particles like electrons do not come back to the initial state of ...
3
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0answers
83 views

How many worlds does the world split into in the Many Worlds Interpretation? [duplicate]

I've been reading up on the Many Worlds Interpretation of Quantum Mechanics, and there is one thing (among many) that I really don't understand. How many worlds are 'created' by an 'observation' or ...
2
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1answer
924 views

Can two photons annihilate?

This is a question about definitions. When two photons interact to create an electron/positron pair, does this process 'count' as annihilation of the photons? I've struggled to find a good ...
3
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2answers
100 views

Identity in quantum operator tutorial

I'm reading this tutorial by Ben Simons entitled Operator methods in quantum mechanics in connection with his course in advanced QM, and I'm a bit puzzled by an identity in page 25, a bit above ...
1
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2answers
2k views

Getting Energies and Probabilities from the Hamiltonian

So I need to find the possible energies and the probabilities of these using the eigenvalues of a Hamiltonian. Once I obtain the eigenvalues, are those the energies E_n in and of themselves? Or do ...
1
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2answers
84 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 ...
2
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2answers
2k views

Determining if a semiconductor is n-type, p-type or intrinsic

The probability that an energy state in the conduction band is occupied by an electron is 0.001. Would this semiconductor then be n-type, p-type, or intrinsic? Notation that I use: $E_F$ represents ...
0
votes
1answer
69 views

How many domains are there in a ferromagnetic material?

How many are there? Also what is the size of those domains? Finally, when domains align with exterior magnetic fields do they move or are they all fixed? I assume they are all fixed because the atoms ...
5
votes
0answers
175 views

Is there a difference between “two photon absorption” and “double quantum transitions”?

Wikipedia has articles on two photon absorption. And a lot of NMR literature refers to double quantum transitions. But is there a difference? As far as I can tell, a double quantum transition is has ...
5
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2answers
219 views

Photon particle/wave question

Imagine a source of photons at the center of a spherical shell of detectors at radius $R$. Assume the photons are emitted one at a time. Now if photons are particles that are highly likely to travel ...
4
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1answer
130 views

Hermitian Operators in time and Measurements

Consider an observable that can be described by a hermitian operator $A$ . No explicit relationship with time is given. What would happen to the probability if the quantity is measured a few days ...
1
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1answer
158 views

Shouldn't the addition of angular momentum be commutative?

I have angular momenta $S=\frac{1}{2}$ for spin, and $I=\frac{1}{2}$ for nuclear angular momentum, which I want to add using the Clebsch-Gordan basis, so the conversion looks like: $$ \begin{align} ...
1
vote
1answer
808 views

Confusion about the probability cloud

What is the meaning of the electron probability cloud? I understood it to mean that the electron has a probability to be found in a certain postion before measurement, but now after reading ...
1
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2answers
181 views

Sign in the time-independent Schrödinger's equation

In the time-independent Schrödinger's equation: $$ -\frac{\hbar^2}{2m} \frac{d^2} {dx^2} u + Vu ~= Eu, $$ why there is a minus sign before the first term?
1
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1answer
64 views

How can enzyme/substrate reactions that adhere (largely) to quantum theory also require 'Newtonian' consideration of gravity?

I'd just like to ask for a little clarification here due to confusion from interdisciplinary studies. I'm currently reading the 1976 paper related to the recent 2013 Nobel Prize for Chemistry, by 2 ...
0
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0answers
134 views

Energy required to demagnetize a soft iron?

How much energy is required to demagnetize a soft iron ferromagnetic material, that has a very low coercive force And a small hysteresis area? Also, would it be possible to demagnetize that same ...
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6answers
3k views

Why won't protons revolve around the nucleus containing electrons and neutrons?

In case of solar system,we can explain "Why Sun would not revolve around any other planet?",by giving the reason that Sun is heavier than any other planets. Heavier the body,greater will be the ...
9
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4answers
2k views

Why is the Copenhagen interpretation of quantum physics the most widely accepted one?

I've been digging a lot into quantum physics in the last few weeks. I didn't care much about the maths, just about what empirically happens to get a conceptual idea about quantum phenomena. The most ...
0
votes
1answer
67 views

In what range the acceleration value of quantum particle lies?

According to Heisenberg's uncertainity principle, the position and velocity of an quantum particle cannot be determined simultaneously. Is it possible to determine position and acceleration ...
5
votes
1answer
893 views

Can we model Chemical Reactions using Quantum Mechanics? If so, what is the most complex reaction we can model?

Not a physicist or Chemist, just interested in QM and it's applications. I've been reading lately about Quantum Chemistry and it occurred to me that since we can model electron orbitals in QM and ...
15
votes
5answers
2k views

Why isn't absolute $0 K$ temperature possible?

So $T$ is defined as $$T = \left(\frac{\partial E}{\partial S}\right)$$ and $S$ is defined as $$S = k_B \ln \Omega$$ where $\Omega$ is the number of accessible states of the system for a given ...
6
votes
5answers
1k views

Infinite Wells and Delta Functions

In considering a delta potential barrier in an infinite well, I can just enforce continuity at the potential barrier-it doesn't have to go to zero. Why then does it need to go to zero at the walls of ...
1
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2answers
677 views

Quantum Mechanics Operator Hermiticity

If $A$ and $B$ are Hermitian operators, show that $$C~:=~i[A,B]$$ is Hermitian too. My work: $$\begin{gather} C=i(AB-BA) \\ \langle\psi\rvert C\lvert\phi\rangle = i\langle\psi\rvert ...
0
votes
1answer
466 views

Hamiltonian operator apply to a wavefunction

When a Hamiltonian operator apply to a wavefunction, how could we write the hamiltonian as, $$H \psi = (E_n-\hbar \omega_0) \psi \ \ ? $$ Is this because $E_n= H+ \hbar \omega_0$? where ...
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2answers
280 views

Oscillation of a Bose Einstein condensate in a harmonical trap

We were asked to try to make a theoretical description of the following phenomenon: Imagine a 2D Bose Einstein condensate in equilibrium in an harmonical trap with frequency $\omega$. Suddenly the ...
0
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1answer
1k views

Why is the wave function complex? [duplicate]

Why should an equation (TDSE) in which first time derivative is related to second space derivative have a solution that contains $i$?The wave function is supposed to be complex, but I am unable to ...
2
votes
1answer
612 views

Why is classical physics not valid for a harmonic oscillator in its lowest energy state? [closed]

I am reading Born's interpretation of wave function in quantum physics by Eisberg & Resnick and I am not able to understand this description about comparison between the classical and quantum ...
0
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2answers
522 views

Which is more characteristic of an element absorption or emission spectrum?

Absorption and emission spectrum are used to reveal the identity of an element and even to find new elements. But, which of them is more characteristic? The mission spectrum would have more lines ...