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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How to know if a wave function is physically acceptable solution of a Schrödinger equation?

How does one decide whether a wave function is a physically acceptable solution of the Schrödinger equation? For example: $\tan x$ , $\sin x$, $1/x$, and so on.
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14 views

Wave Equation Variables and Interpretation

Consider the scalar wave function $\exp[i(kr -\omega t)]$, where $k$ is the wave number and $r$ is the spatial coordinate. We can alternately define $k$ to be a vector that gives the direction and ...
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0answers
19 views

Symmetry Group of system to a given Hamiltonian

I want to determine the symmetry group of the following system: I consider a charged particle in a spherically symmetric potential $V$ and a homogeneous electric field of magnitude $E$ in ...
2
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2answers
66 views

How to handle the potential $V(x)$ or $V(\phi)$ which is not analytic in QM and QFT

In QM, $$\hat{x}\phi(p)=i\frac{\partial}{\partial p} \phi(p)$$ and when $V(x)$ is an analytic function of $x$, then $$V(\hat{x})\phi(p)=V(i\frac{\partial}{\partial p} )\phi(p)$$ and we can do Taylor ...
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8answers
7k views

Why is quantum entanglement considered to be an active link between particles?

From everything I've read about quantum mechanics and quantum entanglement phenomena, it's not obvious to me why quantum entanglement is considered to be an active link. That is, it's stated every ...
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3answers
50 views

EPR Paradox resolution: the spin is fixed at creation but its measurement isn't?

The Wikipedia article on the EPR paradox uses the example of an electron and positron created from a common source, each moving in an opposite direction to the other. Detector A is used to measure the ...
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5answers
3k views

How can one derive Schrödinger equation?

The Schrödinger equation is the basis to understanding quantum mechanics, but how can one derive it? I asked my instructor but he told me that it came from the experience of Schrödinger and his ...
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2answers
52 views

Point-like nature of particle interaction and wave function non-locality

Let us consider the Hamiltonian for the hydrogen atom $$ ...
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2answers
80 views

Separability of a Hilbert space and its implications for the formalism of QM

In the text I'm using for QM, one of the properties listed for Hilbert space that is a mystery to me is the property that it is separable. Quoted from text (N. Zettili: Quantum Mechanics: Concepts and ...
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2answers
321 views

Bloch wave function orthonormality?

there is this text book that is giving me a hard time for a while now: It shows that Bloch wave functions can be written as $$\Psi_{n\vec{k}}\left(\vec{r}\right) = \frac{1}{\sqrt{V}}e^{i\vec k \vec ...
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3answers
240 views

Some small questions about quantum spin and rotations

I'm studying about quantum-spin (in a syllabus about non-relativistic quantum-mechanics though), but I have some trouble understanding everything. So I would like to ask some small questions, which ...
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3answers
37 views

Conceptualization and modelling of spin

I'm trying to get a decent understanding of the bell inequality, and so am trying to understand spin both conceptually and mathematically. When I picture spin, I imagine a sphere rotating about its ...
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0answers
19 views

Probabilities with a qubit

A two-state quantum system has orthonormal energy eigenstates ψ1 and ψ2, with energy eigenvalues E1 and E2 = E1 + ∆E (∆E > 0). These energy eigenstates form a complete set of wavefunctions for the ...
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3answers
163 views

Can two single particles interfere with each other?

Groups of particles can interfere with one another; In the double slit experiment when measuring single photons at the screen each one arrives at the screen in a random manner and they only show the ...
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2answers
213 views

Measurement of the energy of an atom using a cold substance

An atom was prepared in a superposition of ground state and excited states.I propose to measure the state by coupling the system to a cold enough substance. By cold enough I mean $$kT\ll E_1,$$ where ...
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6answers
2k views

What was the need for doing experiments to prove quantum entanglement?

This question comes from someone who is interested in Physics but with no theoretical background. In 1936, EPR presented the thought experiment which later came to be known and quantum entanglement. ...
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1answer
37 views

Introductory Quantum, trouble with this boundary condition and potential

Working on problem 2.40 from Griffiths but can't seem to understand the first boundary condition. We are given the potential $V(x) = \left\{\begin{matrix} \infty & x < 0\\ ...
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0answers
14 views

States in valence and conduction band

I often see a Hamiltonian in second quantization written for the valence and conduction band. Now, I was wondering: What are the single-electron states that form the prouct state they act on? So what ...
2
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1answer
115 views

Proof of the conservation of the energy functional for the Gross-Pitaevskii equation?

From the Gross-Pitaevskii equation \begin{equation}i\hbar\frac{\partial\psi}{\partial t}=\left(-\frac{\hbar^2}{2m}\nabla^2+V+g|\psi|^2\right)\psi\end{equation} using the variational relation ...
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0answers
12 views

Excitation probability given pulse bandwidth and atom linewidth

Consider photon source producing photon pulses with a frequency distribution $f(\omega)$ and a glass tube filled with a gas. The atoms of the gas can be excited by photons with a frequency of ...
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1answer
92 views

Visualisation of electron

first things first, I'm not by any means a physicist nor a student of physics. I study graphic design. Theme of my bachelor thesis is visualisation of physical and mathematical phenomenons, long story ...
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3answers
61 views

Complexity of a physical system

Are there any accepted definitions quantifying the complexity of: a) macroscopic, classical mechanical systems (e.g., a bicycle) b) microscopic systems (ensembles of atoms)? By the way, I'm not ...
3
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1answer
105 views

1D Finite potential well: solutions with $\sinh$ and $\cosh$?

So I am studying the (one dimensional) quantum mechanical finite potential well defined by: $$ V(x) = \cases{0, &|x|>a\cr -V_0, &|x|<a} $$ where $V_0>0$ is a real number. I know ...
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1answer
27 views

Restrictions on Bell-type inequalities

While deriving and proving Bell-type inequalities of the form $|E(a,b)-E(a,b')|+|E(a',b)+E(a',b')|\leq 2$ I know that the conditions on the operators $O_a$ and $O_b$ are that they must be bounded ...
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1answer
62 views

Atom in a box and collapse of the wave-function

Suppose I have an atom trapped in an optically transparent box. I'm assuming the atom is bouncing off of the walls and not bonding, i.e. the center of mass of the atom experiences a square well. Now ...
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2answers
37 views

What role does the Higgs Field play in the universe?

The Higgs field is known as a physical field that covers the entire universe, giving particles their mass. However, that got me thinking if the Higgs field not only gives mass to other particles, but ...
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23 views

Cohen Tannoudji solutions to exercises

Does anyone know where to find the solutions to the exercises of Cohen-Tannoudji's Quantum Mechanics? I am gonna try to do all of them and would like to check.
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2answers
194 views

Is there any physical quantity that does not have uncertainty?

I saw this video and I got a thought: Is there any physical quantity that does not have uncertainty? Basic models are: for lenght for time end energy (so for mass too) and I realized that ...
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1answer
33 views

Would a semiconductor shined with monochromatic laser light matching its band-gap have a 100% efficiency if all of the light was absorbed & converted?

The idea of transporting power through laser light is an interesting area of research. Conversions of up to 54% have been reported for long distance transmission. I would assume ...
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1answer
39 views

Change in Shannon entropy of a quantum circuit of Hadamard gate and a loop

The following Q&A about reversible computing is available here. It has listed a number of practical scenarios where a reversible circuit can still be dissipating heat. Let's assume that none of ...
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261 views
+250

Horrifying electron gas model

I am given the Hamiltonian, in an exercise called plasmons, and where $\langle, \rangle $ denotes the expectation value. $$ H = \sum_{k} \varepsilon_k a_k^{\dagger} a_k + \sum_{k_1,k_2,q} V_q ...
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2answers
115 views

How do we know that photon entanglement isn't the result of the photons's states being predetermined?

I know there is evidence that it is not predetermined and I tried reading articles on it but most of them either don't explain the intuition behind the experiment or they speak in a foreign language ...
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1answer
110 views

Deriving a Useful Solution of the Schrödinger Equation [on hold]

How does one derive the fact that $$\psi(t,x) = (\tfrac{2 \pi \hbar t}{m})^{-d/2}\int_{\mathbb{R}^d} e^{im\tfrac{(x-y)^2}{2\hbar t}}\psi_0(y)dy$$ is a solution of the time-dependent Schrödinger ...
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1answer
51 views

Why doesn't the electron lose or absorb energy while remaining in a selected orbit?

Postulate 2: When an electron revolves in any selected orbits, it neither emits nor absorbs energy . The energy of an electron in a particular orbit remains constant. Thus, Bohr, by postulating ...
3
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2answers
73 views

Importance of Kronecker product in quantum computation

To get product state of two states $|\phi \rangle$ and $|\psi \rangle$, we use Kronecker product $|\phi \rangle \otimes |\psi \rangle$. Instead of Kronecker product $\otimes$, can we use Cartesian ...
3
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4answers
120 views

Virtual particles/quantum tunneling - conservation of energy?

I'm confused as to how the above phenomena can take place since arent they breaking the law of conservation of energy (even, if temporarily)?
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3answers
2k views

What do we see while watching light? Waves or particles?

I'm trying to understand quantum physics. I'm pretty familiar with it but I can't decide what counts as observing to cause particle behave (at least when it's about lights). So the question is what do ...
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0answers
28 views

How to derive a new form of Hamiltonian operator in quantum mechanics using canonical commutation relation?

How does one derive $$\hat{H} = \frac{1}{2}\hat{p}^2m(\hat{q}) - \frac{i}{2}\hat{p}\frac{m'(\hat{q})}{m^2(\hat{q})} + V(\hat{q})$$ from hamiltonian $$\hat{H} = \hat{p}\frac{1}{2m(\hat{q})}\hat{p} + ...
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0answers
16 views

Quantum harmonic oscillator doughnut shape

When phase-space trajectory is plotted for classical harmonic oscillator for p(t)=mx0ωcos(ωt +δ0), a circle is obtained. When done same for the quantum harmonic oscillator, why do we get a doughnut ...
2
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1answer
60 views

Why does the raising and lowering operator not affect total angular momentum?

My notes define: $$ L_{\pm} = L_{x} \pm i L_{y} $$ and states: $$ [L_{z},L_{\pm}] = \pm \hbar L_{\pm} $$ I'm fine with this as it's easy to show the result with some ugly algebra. It then says: ...
3
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1answer
51 views

Does Bell's inequalities also rule out non-computable local hidden variable theories?

I have beenn reading different articles on Bell's assumptions and interpretations, including superdeterminsm. I always end up dizzy when I try tho think about this specific question, so any hints ...
2
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1answer
45 views

Energy in harmonic oscillator [on hold]

The expectation value of the potential energy is exactly half the total according to Griffiths. Is that case always true for quantum harmonic oscillator? Is that the case also for classical harmonic ...
0
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1answer
61 views

How to construct this oracle quantum gate?

I was reading the paper Quantum Computational Complexity in the Presence of Closed Timelike Curves. In this the author mentions that following quantum oracle gate which operates on $n+1$ qubits, can ...
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1answer
42 views

Constructing matrix for spin in Stern-Gerlach experiment for arbitrary angle

This is a conceptual question about a problem in Sakurai. I understand how to solve the problem, but there's something about it that irks me, and it feels like I'm missing something. In the problem, ...
0
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2answers
59 views

Collapse of the wave function and Heisenberg uncertainty

I have been studying quantum mechanics for a few weeks, in particular wave mechanics, as created by Schrodinger, and his equation. As a high school student, I haven't found an answer to this question ...
2
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4answers
870 views

Which Schrödinger equation is correct?

In the coordinate representation, in 1D, the wave function depends on space and time, $\Psi(x,t)$, accordingly the time dependent Schrödinger equation is $$H\Psi(x,t) = ...
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1answer
39 views

Do entangled particles lose entanglement after polarizing filters?

If two entangled particles are sent through different polarizing filters, do they lose their entanglement after the filters?
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3answers
105 views

Why every state evolving infinite time becomes the ground state in QFT?

For any state $|\phi \rangle $ evolving infinite time $$\lim\limits_{t\rightarrow \infty} e^{-iHt}|\phi\rangle=\lim\limits_{t\rightarrow \infty} e^{-iHt}|n\rangle\langle n|\phi\rangle$$ Let ...
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1answer
30 views

Eigenvalues of Angular Momentum in Quantum Mechanics

The eigenvalue equation of the $L^2$ operator is given by $$L^2f_l^m = \hbar ^2l(l+1)f_l^m$$ Side: So a determinate state for some observable $Q$ is a state where every measurement of $Q$ returns ...
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0answers
236 views

Why discrepancies in the Schrödinger equation? [duplicate]

Why is there seemingly two definitions of the Schrödinger equation? \begin{equation} i\hbar\frac{\partial}{\partial t}\Psi=\hat H\Psi. \end{equation} And \begin{equation} i\hbar ...