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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13 views

Wave-like description of Compton scattering and photoelectric effect

I have found in the wikipedia page for QFT the following statement: ... Although the photoelectric effect and Compton scattering strongly suggest the existence of the photon, it is now understood ...
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55 views

Interesting (new to me) things in the exposition of Landau's book on QM

In section I.1 (The uncertainty principle), a principle I already know, the author suggests a "relaxing" picture (Unusual): "We have defined "apparatus" as a physical object which is governed, ...
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1answer
41 views

What is a Hulten potential?

What is the Hulten potential? When is it used? How is it derived? I vaguely heard about in the context of neutron synthesis / quantum mechanics. thanks
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2answers
94 views

Understanding basic quantum mechanics notation

I was talking with a guy about energy levels of an atom in a magnetic field. He said that energy levels are shifted and that, if you want know how much, you have to analyze this: for 1s state: ...
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1answer
76 views

How does vacuum state look in first quantization?

Wikipedia says that the vacuum state is the unit of tensor product. In my understanding then, a first-quantized wavefunction for the vacuum state would be just constant in the each particle's ...
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1answer
32 views

How did phase randomly changed in CHSH test (M. A. Rowe and others)?

Measuring phase of photon should always be randomly changed while checking CHSH inequality, but i can't explain this: http://qudev.ethz.ch/content/courses/QSIT08/pdfs/Rowe01.pdf (the most clear ...
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2answers
64 views

Is it possible that we have a physical state which is a mixture of discrete eigenstates and continuous ones?

For a system has both continuous and discrete spectrum, is it possible that a physical states is something like: ...
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1answer
29 views

Why the first Term is higher in energy than the second?

P. W. Atkins writes in his book "MOLECULAR QUANTUM MECHANICS" in section 9.4 "Term symbols and spectral details" "We shall adopt the convention that the first term is higher in energy than the ...
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1answer
45 views

Expectation value of $a_i^\dagger a_i$ for thermal density matrix

Suppose we have some heat bath with Hamiltonian, $$H=\sum_n \left(a^{\dagger}_na_n+\frac{1}{2}\right)\hbar\omega_n$$ and a density matrix $\rho=Z\exp(-\beta H)$ for some normalisation $Z$. ...
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45 views

What does the wavefunction actually show?

I.e. when someone says they've solved the Schrödinger equation for something, or that the equation can be used to show how the wave function develops over time, what do they mean? I know that its to ...
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1answer
77 views

$\sigma$-additivity of Probability and Quantum Mechanics

$\sigma$-additivity - probability of a sum of countable number of pairly disjoint events equals a sum of probabilities of these events. (3. Axiom of Probability) For pairly disjoint sets $A_k$ ...
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1answer
24 views

The expectation value of the spin of a proton which is entangled

Suppose we have the Bell state $$|\text{ }\psi\rangle=\frac{1}{\sqrt{2}}\left(|\uparrow\rangle_1|\downarrow\rangle_2+|\downarrow\rangle_1|\uparrow\rangle_2\right)$$ and denote the spin operator of the ...
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2answers
71 views

What's the difference between hopping and tunneling?

My professor made a distinction between electron hopping (the closest wikipedia had an article on) and tunneling, saying that one (he didn't say which, but I assume hopping) was temperature dependent ...
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3answers
71 views

Is the uncertainity principle a practical reality, a theoretical law or a measurement problem?

I understand we cannot state with arbitrary precision the position and momentum of a micro-particle as we superpose infinite waves to create a wave packet at the exact position of the particle and ...
1
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1answer
70 views

How to choose the Correct Green's Function?

In order to solve the Green’s function of the Helmholtz operator $$(\nabla^2+k^2)G(\vec r-\vec r’)=\delta^{(3)} (\vec r-\vec r’)$$ one can obtain four different Green’s functions corresponding to four ...
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7answers
2k views

Does electron being many places at the same time violate Physics laws?

The following passage has been extracted from the book Parallel Worlds, by Michio Kaku: Because of uncertainty, the electron does not exist at any single point, but exists in all possible ...
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3answers
179 views

How to derive $[x_i, F(\vec p)] = i \hbar \frac {\partial F(\vec p)}{\partial p_i}$

Wikipedia indicates that the following relation is "easily shown": $[x_i, F(\vec p)] = i \hbar \frac {\partial F(\vec p)}{\partial p_i}$, however I'm having some trouble showing it. I think I'm just ...
2
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3answers
160 views

What is the best article presenting counterarguments to a many-world interpretation? [duplicate]

I'd like to see a clear overview of why the many-world interpretation (WWI) of quantum is wrong, written by someone who believes that. This would be aimed at a technically aware audience, yet as an ...
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3answers
77 views

Intuition on positive-operator valued measures (POVM)

I'm having a little trouble understanding what positive-operator valued measure (POVM) are- in particular why/how they are non-negative. For instance, if they just represent measurements, what about ...
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3answers
48 views

Is a gapless system always conducting and a gapped system insulating?

In an answer to this question, @user566 mentioned that there is a qualitative difference between gapped and gapless systems; that gapless systems are conducting and gapped system are insulating. Is ...
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0answers
37 views

Wigner function for position eigenstates

What is the Wigner function (or $P$ or $Q$ function) associated with $|x\rangle\langle x|$? Thanks for any suggestion.
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2answers
105 views

Particle in a Box: Energy Less than the Potential Energy

I am reading quantum mechanics from Shankar's Principles of Quantum Mechanics. On page 157 he defines the box potential $V(x)$ as $$ V(x) = \left\{ \begin{array}{rl} 0 &\mbox{ if $|x|< L/2$} ...
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1answer
46 views

How can an electron be fired at a target when uncertainty principle says it will spread out around axis of motion?

Consider an electron fired at a target. Taking the axis of motion to be $x$, and position to be $(x,y,z)$ then $\Delta y = \Delta z = 0$ Therefore by the uncertainty principle $\Delta p_y = ...
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0answers
26 views

Quadrupole moment of a valence proton

The state of an unpaired nucleon in the nuclear shell model is given by the quantum numbers $l$, $s$, $j$ and $m_j$ resulting from coupling $l$ and $s$ when we add spin-orbit interaction. In chapter 5 ...
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1answer
42 views

Why does Fermi level has a probability density of 1/2 while it may lie in the forbidden region?

I dont understand how there is a continuous probability density function in semiconductors, when there are several regions which are restricted by Energy, i.e. forbidden energies. Well i know that in ...
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29 views

What are the “name” and “coname” of operators?

So, I've been reading articles about categorical quantum mechanics, and I keep coming across definitions of "name" and "coname" of an operator. Googling these basically only turn up the papers I've ...
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2answers
88 views

What does volume means at the quantum level?

The volume of the electron is the space bounds in which it is contained says the @CuriousOne. But how can we define the volume in such a small range. If we immerse a cuboid into a vessel full of ...
2
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1answer
77 views

Why does Dirac write $\langle\xi'|\overline{f(\xi)} = \overline f(\xi ')\langle\xi'|$?

Starting on page 41 of Dirac's The Principles of Quantum Mechanics, he defines $f(\xi)$ in general to be that linear operator which satisfies $$f(\xi)|\xi'\rangle = f(\xi')|\xi'\rangle\tag {34}$$ ...
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1answer
102 views

Quantum harmonic oscillator solved by analytic method using Schrödinger equation and wave function

I'm having trouble understanding the recursion formula. Using $\xi \equiv \sqrt{m\omega/\hbar}x$ and $K = 2E/\hbar\omega$, the time-independent Schrödinger equation becomes $$\frac{d^2\psi}{d\xi ^2} ...
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4answers
648 views

Why do electrons in an atom occupy only the stationary states?

When we talk about the elementary problems in quantum mechanics like particle in a box, we first calculate the energy eigen-function. Then we say that the most general state is the linear combination ...
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1answer
70 views

Turning a finite difference equation into code (2d Schrodinger equation)

I am trying to convert the following finite difference equations into code (taken from the bottom of page 12 of this thesis by Maike Schulte Numerical Solution of the Schrodinger Equation on Unbounded ...
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1answer
27 views

How much measurements are usually done to test CHSH inequality?

How much times particle is measured during experiment? How much times sub-experiment (state of detector) is randomly changed? Where i can find such statistic?
2
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1answer
75 views

Floquet quasienergy spectrum, continuous or discrete?

I haven't got a feeling about Floquet quasienergy, although it is talked by many people these days. Floquet theorem: Consider a Hamiltonian which is time periodic $H(t)=H(t+\tau)$. The Floquet ...
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44 views

When is the product of a hermitian unitary and another unitary hermitian?

I have a Hermitian unitary $\hat{H}$ and I want to know, if $\hat{U}$ is some other unitary, when is $\hat{H}\hat{U}$ a Hermitian unitary? Specifically, what are the conditions on $\hat{U}$? I know ...
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0answers
51 views

Find Equation of Motion given Hamiltonian

So I am given a harmonic oscillator in an electric field. At $t=0$, we are given that the oscillator is in the ground state. The Hamiltonian is: $$H=\hbar \omega[a^{\dagger}a+\frac12+\kappa ...
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1answer
60 views

How do we perform transverse measurements in a two level system?

In quantum mechanics any two level system can be mapped onto effective spin variables. If the system is defined by two energy levels, $|E_1\rangle$ and $|E_2\rangle$, the Hamiltonian is $$ H = ...
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12 views

What are some good books that link quantum mechanics with concepts such as fate, coincidence and free will? [migrated]

I am more interested in a high level conceptual approach than the quantitative one that talks about how quantum mechanics is/is not relevant to concepts such as what I mentioned above, and why. ...
1
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1answer
30 views

anti-symmetric spin wave function of $|^3\text{He}\rangle$

Consider $|^3\text{He}\rangle$ in the ground state (2 protons and 1 neutron). Assume the spatial part of the wave function is symmetric. I have to construct the spin part of the wave function. This is ...
4
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3answers
267 views

How is a bound state defined in quantum mechanics?

How is a bound state defined in quantum mechanics for states which are not eigenstates of the Hamiltonian i.e. which do not have definite energies? Can a superposition state like ...
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2answers
59 views

Particle wave duality question: 2 different detectors observing different properties?

I hear a lot of people saying an observation of the double slit experiement collapses the wave function and doesn't allow you to view the particle in 2 places at the same time or as both wave and ...
1
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1answer
66 views

why non orthogonal states are indistinguishable?

I want to know what does it mean by distinguishable quantum state from Mathematics perspective I mean mathematically. As a non physics background student could any one explain me why non orthogonal ...
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1answer
52 views

Why is it said that the Heisenberg model is a hard-core boson model?

I am confused as to why it is said that the Heisenberg model is a hard-core boson model.
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1answer
46 views

Tetrad choice for Pauli-Lubanski in the massless case

The Pauli-Lubanski pseudovector coincides with intrinsic spin in the rest frame of the particle. In a more general frame, one defines a tetrad and projects the PL vector on it to define intrinsic spin ...
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1answer
27 views

Translational operator on potential

In https://wiki.oulu.fi/download/attachments/14553161/lattice.pdf I have a problem with the translational operator: The second line under the first figure says $$\tau^\dagger(a)V(x)\tau(a)=V(x+a).$$ ...
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2answers
40 views

Hamiltonian split into Mass term and Decay Width

I have encountered the following procedure several times now, and none of the sources ever explain the physical reason behind it: The Hamiltonian $H$ is split into $M$ and $\Gamma$. WHY? Where ...
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0answers
43 views

When can you apply Ehrenfest's theorem?

I know when the initial state ($\Psi(x,0)$) is given, $\frac{d\langle x\rangle}{dt} \not=$ $\langle p\rangle $. I thought you can only apply Ehrenfest's theorem when $\Psi$ is a function of $x$ and ...
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42 views

Quantum master equation

In the framework of Redfield Quantum Master Equation, the popular approach is to use a tight-binding model linear conductor for the modeling of the Fermionic bath. Does someone can refer me to more ...
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1answer
60 views

How do we find the canonical ensemble density matrix for two spins?

A compound system is constructed by two coupling spins, and the Hamiltonian is $$ \hat H = -J\hat\sigma_1·\hat\sigma_2 - \mu_\mathbf{B}\big( \hat\sigma_{1z}+\hat\sigma_{2z} \big)B. $$ So, how ...
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0answers
53 views

Definition of spatial and temporal coherence in QM?

It is often said that lasers are spatially and temporally coherent. Is there a simple definition of spatial and temporal coherence in the language of quantum mechanics? More specifically, can these be ...
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2answers
74 views

Physical interpretation of applying a unitary operator to a state

When we apply one of the Pauli matrices $\sigma_y$ on one of its eigen-vectors $| \odot \rangle$, what does the eigen-value tell us about $| \odot \rangle$? Is this considered a measurement of $| ...