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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128 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
45 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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66 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 ...
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2answers
74 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 ...
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1answer
113 views

Deriving a Useful Solution of the Schrödinger Equation [closed]

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
44 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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237 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 ...
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2answers
95 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 ...
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3answers
114 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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0answers
24 views

With what fraction photon quanta emission rate is decreased in the expanding universe? [closed]

Light from edge of the observable universe has travelled 13.8 billion light years so far. And, that edge itself has travelled 32.2-33.2 billion light years (that's why actual radius of observable ...
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2answers
75 views

Quasiclassical QM for central fields

Let's have quasiclassical QM for central field $V(r)$. The Schroedinger equation for radial part of wavefunction $R_{nl}$ after substitution $u_{nl} = rR_{nl}$ takes the form $$ u_{nl}{''} + ...
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85 views

State vector vs density operator

We formulate quantum mechanics using language of state vectors. One alternative formulation is possible using density operator or density matrix. Why we are doing this alternative approach? Is the ...
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83 views

What is the most agreed upon quantum mechanical equation of motion?

On multiple Wikipedia articles, it mentions several quantum mechanical equations of motion, namely those by Schrödinger and Heisenberg. Which one is the most accurate and agreed upon quantum ...
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1answer
78 views

Eigenvalues of hamiltonian [closed]

Q: THe hamiltonian which describes the motion of a particle in an one dimensional potential V(x) is $H_0=\frac{p^2}{2m}+V(x)$ , where $p=-i\hbar \frac{d}{dx}$ is the momentum operator. $E_n^0$ , ...
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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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2answers
54 views

Can Quantum Entanglement and Quantum Superposition be considered the same phenomenon?

Quantum entanglement is known to be the exchange of quantum information between two particles at a distance, while quantum superposition is known to be the uncertainty of a particle (or particles) ...
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2answers
74 views

Creation and annihilation operators in Hamiltonian

If I find a Hamiltonian $H = \sum_{k} \varepsilon_k a_k^{\dagger} a_k + \sum_k V_k a_k^{\dagger} a_k$ then I was wondering: As far as I know this is many body theory and so these operators act on ...
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375 views

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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0answers
36 views

Larmor Precession of a macroscopic number of electrons

I know that there are some similiar questions out there, but I'm still quite puzzled by the following problem. Say i have a box full of interacting electrons ( I'm not sure if it would change anything ...
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0answers
101 views

Are there eight or four independt solutions of the Dirac equation?

I edited the question as a result of the discussion in the comments. Originally my quesiton was how to interpret the four discarded solutions. Now I'm making a step back and hope that someone can ...
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55 views

What is really interacting in weak interactions?

Only particles with chirality $-1$ do interact weakly. The corresponding eigenstate in the Dirac basis is $ \Psi_L = \begin{pmatrix}f \\ -f \end{pmatrix} = \begin{pmatrix}u_r {\mathrm{e}}^{-imt} \\ ...
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1answer
46 views

Wave packets and half-width at half-maximum

Suppose we have a Gaussian wave function and amplitude distribution function $$\psi(x) = (\frac{2}{\pi a^{2}})^{1/4}e^{-x^{2}/a^{2}}e^{ik_{0}x}, \qquad \phi(k) = (\frac{a^{2}}{2\pi})^{1/4}e^{-a^{2} ...
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3answers
156 views

Root of $i$, which one to take?

The propagator of a free particle in 1d is $$ K(x_b, t_b; x_a, t_a ) = \sqrt{\frac{m}{2\pi i \hbar (t_b-t_a)}} \exp \left [ \frac{i m (x_b-x_a)^2}{2 \hbar (t_b-t_a)} \quad \right ] .$$ It looks ...
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1answer
47 views

Integration of $e^{-it\sqrt{\mathbf{p}^2 + m^2}}$ for QM amplitude

My question might be more about maths than physics, but it originated in a Physics context. Take $\hbar$ = $c$ = 1. I was looking at the amplitude for a free particle to propagate from an initial ...
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3answers
536 views

New subatomic particles

In reference to the findings talked about here http://online.wsj.com/articles/two-new-subatomic-particles-found-using-large-hadron-collider-scientists-say-1416409980 and other similar articles ...
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2answers
72 views

How can one be 'certain' about anything that has an “Uncertainty Principle” at its core? [closed]

The Uncertainty Principle, which says that more than one aspect of a particle cannot be measured simultaneously, illustrates one of several major differences between quantum physics and classical ...
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1answer
34 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
46 views

Why do silicon solar cells only produce ~0.6v when the band gap of silicon is ~1.1v?

I've been researching into this and can't quite figure out where that lost voltage is going. When silicon is excited by a photon within its absorption spectrum, it will always have an internal ...
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0answers
57 views

Quantum Entropy-a minimization problem

I came upon this (not homework) problem of minimizing the following expression ...
0
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1answer
34 views

Spin operator eigenstate in Fock space

I am creating an operator group from representation of spin 1 operators $$J_{x} = \frac{1}{\sqrt{2}}\left(\begin{array}{ccc} 0 & 1 & 0\\ 1 & 0 & 1\\ 0 & 1 & 0 \end{array} ...
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2answers
30 views

How is light trajectory affected by the trajectory of environment it passes through?

There's a sci-fi concept of slow light that I find very amazing: Imagine a glass material that has index of refraction $n$ say, $3,000,000,000$ which means: $$v_{glass} = \frac{c_{vacuum}}{n} = ...
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1answer
36 views

Density matrix: error with diagonalization claim and fixing it

On page 174 of Townsend's "A Modern Approach to Quantum Mechanics", 2nd edition, it says the following: "For a mixed state, one for which $p_k$ is the probability that a particle is in the state ...
0
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1answer
18 views

Does a photo-excited semiconductor produce a constant voltage output equal to the band gap?

Does the voltage produced by a photo-excited semiconductor always equal the band gap of that semiconductor, or does the voltage vary over a range similar to the photon energies in the emission spectra ...
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1answer
21 views

Electrical Generator [duplicate]

I have seen the generator that produces electricity from the earth's magnetic field demonstrated I have a video if it working It was taken approximately 15 years ago in California
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2answers
60 views

How do we know if distant stars we see by their light are real objects? [closed]

Is there a way to be sure if they are not just light, but real objects?
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3answers
111 views

A misunderstanding regarding infinite square well

Here is a picture of the energy states of infinite potential well. We can see That the first level have a half wavelength which fittes with a full wave of the second level. $$\frac{ \lambda _{1} ...
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60 views

Is quantum uncertainty a function of how matter is distributed in the universe?

As an outcome of his PhD thesis work, Richard Feynman and John Wheeler wrote a series of papers on how the kickback on an electron as it emits a photon can be modeled accurately as the result of an ...
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1answer
26 views

What happens to K.E. in matter antimatter annihilation?

If I have two matter and antimatter particles, say an electron and a positron, each moving towards each other with a certain speed, they annihilate after the collision. Does the energy of the photons ...
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24 views

Can we use combined symmetry to simplify the calculation of algebraic PSGs?

In classifying mean-field spin liquids under projective construction, the algebraic projective symmetry group (PSG) approach focus on the mathematical construction of the possible extensions of the ...
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33 views

Finding the expectation value of the annihilation operator with respect to a given state

Using dirac notation we were given a state vector $$|\Psi(t=0)\rangle = A\sum\limits_{q=0}^Q \frac{1}{(q+i)} |\phi_q\rangle$$ Where $\phi$ is part of a complete orthonormal set. I found the ...
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2answers
74 views

why do metals feel cold when electron moves at Fermi velocity?

This might be a very elementary question. Considering that electrons in typical metals have very high Fermi velocity, why is it that when you touch a metal you feel cold? My intuition tells me that ...
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21 views

space representation of a local potential

Why is it that for a local potential $V$: $$\langle x | V | x' \rangle = V(x) \langle x | x' \rangle = V(x) \delta(x - x')$$ I saw this being used in a book but without any explanation. The part with ...
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1answer
52 views

Superposition and simultaneous observation

Trying to understand superposition. Ok, so double slit experiment. The multiple paths the particle simultaneously travels interfere with each other but as it is absorbed, it chooses one "actual" ...
0
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1answer
77 views

Are there any known physical implementations of quantum gates?

I was wondering if there are any known implementations of a small number of quantum gates that can interact with each other. Certainly we don't have a "complete" set of quantum gates (where ...
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1answer
135 views

Do consciousnesses get “scattered” across the many worlds of the MWI?

According the many worlds-interpretation (MWI) of quantum mechanics, following a decision with possible outcomes $A$ and $B$, with respective probabilities $p_A=P(A)$ and $p_B=P(B)$, a proportion ...
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0answers
28 views

Making An Energy Momentum Plot For A Rashba Model (Using Discretization)

I want to make a plot of the Energy versus the Momentum of the Rashba model, using discrete matrices. First Ill show how I did this for the free particle. Subsequently I will show what goes wrong for ...
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2answers
93 views

Bound electrons don't move, right?

I've never been satisfied with the explanation that electrons have a “speed” and move close to the speed of light, thus incurring relativistic effects that make gold pretty and mercury wet. I learned ...
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1answer
44 views

Pressure in Harmonic Oscillation

Classical Harmonic oscillator's energy depends on temperature as it equals $k_B$$T/2$. However, quantum harmonic oscillator energy is $(n+1/2)hf$. So, when T=0, quantum predicts motion. I have been ...
2
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1answer
98 views

Why is quantum tunneling most significant between states of equal energy?

Why is it, that quantum tunneling is only significant between states of nearly equal energy (as claimed here: 'Since tunnelling is significant only between states of nearly equal energy, tunnelling is ...
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0answers
63 views

Commutation relation of a operator with Hamiltonian [duplicate]

Given that the eigenvalues of a Hamiltonian operator $H$ are bounded below, will a Hermitian operator $T$ exist such that $[T, H] = i\hbar{\bf 1}$ identity operator?