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
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Representation of indistinguishability in quantum mechanics

I was wondering that if particles are indistinguishable in quantum mechanics, then why do we still express their states $\left| \uparrow \downarrow \right\rangle$, as meaning particle 1 (in the first ...
0
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2answers
130 views

Which is the most fundamental constant between the Planck constant $h$ and the reduced Planck constant $\hbar$?

This question is related to Planck units (also called natural units, absolute units or God's units). I'm wondering which constant is the most fundamental and should be normalized to 1. I would like as ...
2
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0answers
374 views

Coherences in the density matrix

It is said that the off-diagonal elements of density matrix are coherence. When a system interacts with its environment the off-diagonal elements decay and the ...
3
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3answers
723 views

An operator on the other side of the Schrödinger equation

A form of the Schrödinger equation is $$ \left[-\frac{\hbar^2}{2m} \nabla^2 + V(\vec{r}, t)\right]\Psi = i\hbar \frac{\partial}{\partial t} \Psi $$ The bracketed term is of course the ...
4
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1answer
263 views

After using annihilation operator on vacuum state, why it is $0$ instead of vacuum?

For bosonic systems, why $a|0\rangle=0$ and not $a|0\rangle=|0\rangle$?
2
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1answer
43 views

Neutral quantum particle in inhomegeneous magnetic field

I'm trying to understand Stern-Gerlach experiment on a computational level. Suppose we have a neutral particle with magnetic moment (e.g. a neutron), and apply an inhomogeneous magnetic field to it ...
2
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2answers
115 views

Photons and Absorption

Hello and thanks for reading my question: Imagine we send one photon at an atom, and it happens to be the right frequency such that it gets absorbed fully by an electron in this atom. Obviously that ...
0
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0answers
186 views

Gutzwiller mean-field method in Bose Hubbard model

Gutzwiller mean-felid method is an efficient way to study Bose-Hubabrd model in optical lattice with a harmonic trap. Gutzwiller method assumes there is no spatial correlation within the trap, so ...
1
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1answer
164 views

Particle In a Box and momentum, velocity

So on a homework assignment, we are give the width of a well, $a$, and the mass of the particle $m$ and we want to find the average velocity of the particle at the n=1 state. So here is my attempt at ...
2
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4answers
589 views

Why is $ \vec{S}^{(A)} \otimes \vec{S}^{(B)} = \frac{\hbar^2}{4}(\sigma_x \otimes \sigma_x + \sigma_y \otimes\sigma_y + \sigma_z \otimes \sigma_z)$?

I haven't been taught tensor product in class but they have taught us addition of spin. I looked up online in this link->http://homepage.univie.ac.at/reinhold.bertlmann/pdfs/T2_Skript_Ch_7.pdf#page=10 ...
43
votes
9answers
8k views

Why is it said that without quantum mechanics we would not have modern computers?

I've heard this in many quantum mechanics talks and lectures, nevertheless I don't seem to grasp the idea behind it. What I mean is, at which point is that our modern understanding of quantum ...
2
votes
1answer
117 views

On use of Hamiltonians for Helium

The Hamiltonian of helium can be expressed as the sum of two hydrogen Hamiltonians and that of the Coulomb interaction of two electrons. $$\hat H = \hat H_1 + \hat H_2 + \hat H_{1,2}.$$ The wave ...
2
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2answers
163 views

How does one produce entanglement?

In practice, when entangling two particles (say two electrons), is creating an entangled state purely a matter of bringing them close enough together? What I mean is, to make their wave functions ...
2
votes
1answer
626 views

Effective Hamiltonian / Perturbation theory for non-degenerate case

Trying to wrap my head around the following situation. Consider first a case that I understand well: Let's assume a three level system where the lowest two levels are degenerate and individually ...
1
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0answers
68 views

Deriving probability distributions from the Wigner distribution

I know that I can calculate the probability distributions of $x$ and $p$ from the Wigner quasiprobability distribution, and I can calculate the probability distributions of other operators by ...
2
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2answers
1k views

Particle in a 1D Box with Symmetric potential: How find solutions?

I am working on a problem in which I shall find the normalised solution to the 1D particle in a box. Solving for the particle in an asymmetric potential is quite straight forward, but I run into ...
2
votes
3answers
353 views

Do ionisation of atoms release photons?

I was reading through my text book about Fluorescence. It said "inside a fluorescent bulb, the mecury atoms collide with each other and with electrons get excited and ionised. During de-excitation, ...
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0answers
98 views

Time evolution of quantum states

Time evolution of a quantum state is fully described by a one parameter family of unitary operators. What I can't seem to understand is, given some unitary operator acting on some Hilbert space, can ...
3
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1answer
298 views

Why are there gapless excitations in the anti-ferromagnetic Heisenberg model while the true ground state is a singlet?

The true ground state of the anti ferromagnetic quantum Heisenberg Model (nearest neighbor only)is known to be a singlet (I think this is Liebs theorem.) Since a singlet is invariant under rotations, ...
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2answers
533 views

How to determine a strong or weak interaction (Strange particles)?

As you know $\pi^-$ meson + proton ---> $K^+$ meson + $\Sigma^-$ particle. (AntiUp,down) + (up up down) --> (up antistrange) + (down down strange) I know that the quark number has be conserved in ...
0
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1answer
77 views

relation between photon number and energy

Suppose there are two light beams. One is red while the other is violet. The energy of both is the same. Which one of these beams has a larger number of photons, or is the number of photons relevant? ...
1
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0answers
136 views

Big Bang, Heat Death, and cause and effect

If the Universe has two 'end points', one being the Big Bang, and the other being heat death, is there anything in the laws of physics which forbid a random fluctuation in the heat death state from ...
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0answers
86 views

How to make a base tranformation for a linear operator in QM? [closed]

I have 2 bases A and B with the following kets: Base A: $|a_1\rangle$ and $|a_2\rangle$ Base B: $|b_1\rangle = \frac{1}{\sqrt2} \cdot(|a_1\rangle + i\cdot|a_2\rangle)$ $|b_2\rangle = ...
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votes
2answers
322 views

if the universe is flat does it mean it exists only in our mind as math? [closed]

My dad, who is a retired mathematician, has this attitude, which I think we all have as kids, that ultimately reality is made of stuff. End of story. If you look around yourself in the world, ...
1
vote
2answers
270 views

What does this quantum experiment says about quantum world?

I am complete noob so please bear with me. I always read that in quantum world things exists as probability and only become one when they are observed...or wave collapses into particle. But there was ...
3
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1answer
87 views

Using the fine structure constant to measure atomic and molecular sizes

This is kind of a coursework question but it bring up some really interesting things about the fine structure constant $\alpha$ so I wanted to post it to not only make sure I understood something but ...
9
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1answer
261 views

Interpretation of the Instanton in SUSY QM

This is a loose follow up to this question: Interpreting Argyres' spectrum of spontaneously broken SUSY QM. In SUSY QM, the Hamiltonian can be cast as a 2x2 matrix $$ H = \frac{1}{2}p^2 + ...
5
votes
1answer
195 views

Energy fluctuations in quantum canonical ensemble

How would you go about showing that in the quantum canonical ensemble (that is, in the density matrix and operator formulation), the energy fluctuations, namely $\langle H^2\rangle - \langle ...
2
votes
0answers
51 views

Can someone explain to me the Rocksar-Kivelson Hamiltonian?

The following paper shows the hamiltonian of the 2D quantum dimer gas (page 2) http://www-thphys.physics.ox.ac.uk/people/ClaudioCastelnovo/Talks/050209_MIT.pdf Here are some questions I have. Why ...
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0answers
42 views

Subnuclear physics vs wave function

This question is more a philosophical question than a physics one. When we appreciate particle physics we study that in order to explain some experimental results we have to introduce a new particle ...
1
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1answer
242 views

Nonzero ground state energy of the quantum harmonic oscillator [duplicate]

Since $\frac{1}{2}\hbar \omega$ is the zero point energy of the ground state of the harmonic oscillator, then there is no way to extract this energy. Therefore, in what way is this value different ...
0
votes
1answer
123 views

Is it possible to find the hydrogen atom's radial wavefunctions?

Is there a way to actually find the equation of $R(r)$ without looking at a table with these equations already given? I'm given $n$, $\ell$, and $m$.
6
votes
1answer
115 views

Quantum Logic and Quantum Field Theory

Quantum Logic is a very interesting and powerful answer to the problem of Quantum Mechanics foundations. Nevertheless this approach is usually developed in a non-relativistic framework. Is it still ...
6
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2answers
99 views

Energy in electromagnetic radiation

I learned that power intensity in EM (electromagnetic) radiation is $$ I=\frac12c\varepsilon_0E_0^2 $$ This equation implies that the energy in EM radiation is frequency-independent I also learned ...
2
votes
2answers
156 views

Uncertainty principle

Think of a particle known to be trapped in a box of size $\Delta x$ and cooled down to near absolute zero. I know that attempting to measure the momentum of this particle repeatedly will give a random ...
2
votes
1answer
75 views

Light Waves and Light Photons gedanken Experiment

Suppose you have a source of light that emits light with a wavelength of 2 meters, and you set the device to be turned on and switched off alternately. You also set it so that each interval the device ...
0
votes
3answers
230 views

Ground state of hydrogen atom

My interpretation: When we have no angular momentum, the potential well looks like this, my question is: How do you find the point where the wavefunction penetrates its classical forbidden region, ...
-1
votes
1answer
44 views

Atoms and their bonds in an explosion

I was watching a video and when the car did blow up I asked to me... what happens with the atoms and their bonds when an object blows up of this way? what is the behavior of the atoms and their bonds ...
4
votes
2answers
320 views

Are nodes and orbitals in atoms simply probability distribution clouds or are they of any physical relevance?

I fail to understand what the electron clouds actually signify. Such as the $p$ orbitals, which have a dumbbell like shape. Now I am aware that they aren't actual trajectories of electrons, but what ...
1
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0answers
60 views

Why is there no interference pattern at D0 in the delayed erasure experiment?

The apparatus below represents an apparatus for the typical delayed erasure experiment. My question is, why is there no interference pattern observed at D0 in this experiment (interference is only ...
0
votes
1answer
413 views

Quantum Mechanics - Finding momentum probability density [closed]

everyone. I got a bit stuck on 2(iii), this is supposed to be a easy question, but i don't know how you get the square term? I thought you just do the Fourier transform, but then I got some ...
3
votes
0answers
75 views

Literature on the time reversal operator

Time reversal symmetry seems to be a very useful concept and is mentioned in a good number of papers I recently came across. Most of the time people claim that a certain system or Hamiltonian is time ...
2
votes
2answers
140 views

Extra energy in quantum tunneling

In quantum tunneling, the probability of finding an electron inside the potential barrier is non zero (http://i.stack.imgur.com/v8Kr1.gif). So we can actually find an electron which had an energy E in ...
3
votes
2answers
203 views

Why do the states of a spin multiplet have to have the same symmetry?

This was said in Prof. Balakrishnan lecture 19 on quantum mechanics for the case of exchange symmetry, but he showed no reason why. For example, the system corresponding to two spin $\frac{1}{2}$ ...
0
votes
1answer
354 views

Why is Heisenberg picture used if Schrödinger picture is simpler?

In Heisenberg picture the operators evolve in time instead of states, which evolve in time in Schrödinger picture. But this also means that to solve the equations (at least numerically) one has to ...
6
votes
4answers
312 views

Why is Spin Less Classical than Position?

It is often repeated that "the spin observable is purely quantum and has no classical counterpart". What is actually meant by that? I see no principle difference between the set of spin observables ...
1
vote
2answers
753 views

Why are Cooper pairs formed by electrons of opposite momentum and spin?

I understand that Cooper pair in low-temperature superconductivity are formed by electron-phonon interaction. Normally one then assumes that electrons of opposite momentum and spin are paired. This is ...
0
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1answer
140 views

Toroidal magnet in Tonomura et al. demonstration of Aharonov-Bohm effect

What does the magnetic field look like in Tonomura's toroidal magnet coated with a superconductor? See this paper to find results showing conclusive proof of the A-B effect and flux quantization. ...
2
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0answers
71 views

Classical/ Quantum mechanical view of magnetic monopoles

Is there any classical/ quantum mechanical proof for the non-existence of magnetic monopoles? Or is it just lack of experimental evidence that has led us to the conclusion that monopoles do not exist, ...
0
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1answer
80 views

Find values of $x$ such that the probability density $|\Psi(x)|^2$ of a wave function is maximized

How do I find the values of $x$ for a given wave function $\Psi(x)$ such that it's probability density function $|\Psi(x)|^2$ will be maximized? My guess is to to constrain the derivative by the ...