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Questions tagged [quantum-mechanics]

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 quantum-field-...

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Could the theory of everything be an algorithm?

I've been thinking about the theory of everything. Could the theory of everything to explain how the universe work be a computer algorithm? Is there any way to test whether the universe is a ...
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Mode in quantum mechanic

Let suppose we have $N$ identical composite particles at ground level. Each composite particle have two distinguishable particles. Thus the state of composite bosons in ground state can be written as ...
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What is the wave nature of electron? [duplicate]

Is electron a standing wave or a probabilistic wave? or is it both? can someone explain me also what wavelength we calculate from de Broglie's equation? also does electron spin around itself? or is ...
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20 views

Max Planck and energy quantization idea

Did Planck have an intuition behind the idea of energy quantization of atomic oscillators and radiation, or it was just a mathematical trick to drive his distribution law?
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What are the conditions for molecular,photon resonance other than same frequency?

I know that the basic condition for molecular,photon resonance is same frequency but what are the other condition for this process like phase relationship,round trip of the molecules and so.Also can ...
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28 views

what kind of information is shared between entangled particles

when two entangled particles are separate by distance . what exactly happens to them , that influence us to consider they connected each other?
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How do Hermitian operators work?

I don't understand the concept of Hermitian operators. For instance, if we take $\hat{Q} = x$. And we want to check it is a HERMITIAN operator, by applying the formula $$\int_{-\infty}^{\infty} f^{*}...
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Quantum synchronization description used in paper

In the paper "Steady-state spin synchronization through the collective motion of trapped ions" it states the following: "Steady-state synchronization of atomic dipoles forms the foundation for ultra-...
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What is the difference between $\vert-\rangle$ and $\vert+\rangle$?

I understand that a Qubit can be represented in the form of $$\vert\psi\rangle=\alpha \vert0\rangle+\beta\vert1\rangle$$ where $\alpha$ and $\beta$ are complex numbers and the $\alpha^2$ and $\beta^2$ ...
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Schrödinger's Clock

I would be grateful for any comments regarding two variations of Schrödinger's Cat experiment I’ve been pondering. In the first, wishing no harm to the animal, I remove the cat and replace it with a ...
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1answer
34 views

Transition Amplitudes

We have a forced SHO Lagrangian : $$L = \frac{\dot{\phi}^2}{2} - \frac{m^2{\phi}^2}{2} + f(t)\phi$$ The external force goes to $0$ at the two infinities. I'm trying to compute : $$ \langle 0|T e^{-i \...
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Adsorption and Emission spectrum [duplicate]

I learned at school today , that if we provide sufficient energy to electron ,it will excite to higher energy state and same dark lines will be obtained in a continuous spectrum. I also learned that ...
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3answers
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Why is $\langle c \cdot f|g\rangle=c^*\langle f|g\rangle$?

Why is $\langle c \cdot f|g\rangle=c^*\langle f|g\rangle$? $c$ is a complex number and $c^*$ is the conjugate. I think that $\langle c \cdot f|g\rangle=c\langle f|g\rangle$ because that's how scalar ...
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Can we observe the cross over between different Dyson ensemble distributions at the same time?

In random matrix theory we randomly choose matrix elements But they should follow certain symmetry properties. According to Wigner there can be 3 distributions GOE,GUE,GSE and these distributions are ...
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UFO SIGHTING 11th September 2004 England RG30 3RR [on hold]

Michael Lewendon here. Know nothing at all about Physics or science. But my wife and I witnessed a Spaceship the size of Wembley Stadium, we watched this for eight minutes or so in broad daylight. If ...
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Can Eugene Wigner's “consciousness causes collapse” interpretation of quantum mechanics be made lorentz invariant?

The Eugene Wigner's interpretation of quantum mechanics is realist interpretation of QM. In this interpretation the wave function is physically real, and wave function collapse is caused by conscious ...
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Continuity equation is guage invariant for a charged particle in electromagnetic field

I know that the Schrodinger equation is gauge invariant but how to show that the continuity equation is also gauge inavariant? Any comments?
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3answers
60 views

Two in-line double-slit experiment

Say you have the classic double slit arrangement for electrons with detectors at the slits to determine which slit an electron passes through. Then the electrons will act as particles after passing ...
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1answer
52 views

Commutator expectation value in Quantum mechanics

Suppose A and B are operators, A is Hermitian and their commutator is the identity operator: ...
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31 views

What are the units for state vectors in QM? [duplicate]

Specifically, it seems that a state vector should be dimensionless because: $| \langle \psi | \psi \rangle |^2$ is a probability which is dimensionless However, I find myself doing manipulations ...
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1answer
27 views

Why does classical light (arbitrary mixtures of coherent states) always result in super-Poissonian statistics?

It is a well-known result that classical light (which I take here to mean mixtures of coherent states) cannot produce sub-Poissonian photon-counting statistics, with a single beam of coherent light ...
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Momentum operator of the electromagnetic field in terms of the anhilators operators

According to Townsends'book I obtain the result of P in terms of the annihilation operators but partially since, when it comes to calculating there are 4 terms, two of which involve operator of the ...
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3answers
51 views

What exactly is a hyperfine level as mentioned in the definition of a second?

I have a quite simple question: What exactly is a hyperfine level (or a hyperfine structure)? Maybe my question sounds (or is) stupid $-$ I am not an expert in physics $-$ but I didn't find any ...
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Magnetic dipole moment operator

I have a question. I have a exercise in QM and don't know how to do it. M is Magnetic dipole moment operator of a system that has spin 1/2. A set of measurements allow to know the following ...
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2answers
36 views

Quickly write a unitary transformation connecting two arbitrary states

This is for an introductory QM course. Say, I have pure states $\vert\alpha\rangle$ and $\vert\beta\rangle$. I would like to find a unitary operator that takes me from one to the other. What is the ...
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1answer
63 views

Tensors and the Klein-Gordon Equation

Consider the Klein-Gordon equation: \begin{equation} \frac{\partial^2 \psi}{\partial t^2} = c^2 \Delta \psi - \frac{m^2 c^4}{\hbar^2} \psi, \end{equation} and define for each one of its solutions $\...
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How is photonic qubit information extracted from quantum memories?

I want to preface this by saying that I am a high school student participating in the AP Research program, and so while I am doing as much individual research as I can in this field, I have no formal ...
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How to find many body states whose total $L_{z}$ eigen values are zero?

I am trying to solve construct matrix representation of Helium atom. The hamiltonian is , $$H=-\frac{1}{2}\sum_{i=1}^{2}\nabla^{2}_{i}-\sum_{i=1}^{2}\frac{2}{r_{i}}+\frac{2}{|\vec{r_{1}}-\vec{r_2}|}$$ ...
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Why states close in energy stay away from each other?

According to random matrix theory in the presence of strong disorder off diagonal elements are suppressed and the states close in energy reside far apart from each other. Why is is so?
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Finding coordinate uncertainty of a particle

I'm given a one-dimensional particle of mass $m$ with "random uncorrelated" $\Delta x_o$ and $\Delta p_o$ and told to find the coordinate uncertainty at time $t$, $\Delta x_t$, then to find the ...
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2answers
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What is meant by unitary time evolution?

According to the time evolution the system changes its state the with the passage of time. Is there any difference between time evolution and unitary time evolution?
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2answers
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Gravitationally-induced slowing-down of the spreading of a wave packet

The spreading of a wave packet is very fast in quantum mechanics: for an electron, a gaussian wave packet spreads from one angström to 600km in one second! In his famous QM book, Sakurai mentions that ...
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Can someone explain how charge stability diagrams work?

Sorry I'm relatively new to this area. I keep seeing figures like the one shown here and I'm unsure how to interpret what it means. What do the numbers (0,0), (1,0) etc. come from, and what causes ...
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1answer
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In a class of parametrized symmetric Hamiltonians, should its symmetry operator be parametrized the same way?

I would like to ask the following in the context of symmetry-protected topological phase. Consider a class of Hamiltonians parametrized by $\{a_1,a_2,...\}$ denoted by $H(a_1,a_2,...)$. All over the ...
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Quantum mechanics inside our body [on hold]

How close are we to explain the biological phenomena such as protein synthesis, mutations, DNA & genes concepts using quantum mechanics?
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64 views

Are there wavefunctions that don't get more localized as we go backwards in time? [duplicate]

Gaussian wave packets spread as the time passes, which means that as we go backwards in time they get more localized. Therefore, Gaussian wave packets introduce less uncertainty in the position as the ...
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What are the different versions of the Schrodinger Wave Equation? [on hold]

Whilst I have been looking at Quantum Mechanics online, I have come across lots of different versions of the SE. What is the difference between them, why are there some with Dirac Notation and others ...
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1answer
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Time evolution operator in QM

I am reading a introduction to quantum mechanics right now. There is a part about the time evolution operator: \begin{align*} i\hbar \partial_t \,\psi(\vec r, t) = \hat H(t)\, \psi(\vec r,t) \end{...
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Nature of electron or our weakness? [duplicate]

We say that we cant know the position of an electron. Is this because of the nature of electron to behave like a probability wave or our weakess to identify the "equation" of its position ?
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1answer
22 views

What is the Quantum interference? [on hold]

Can someone please explain what is Quantum interference and how it differs from classical interference
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1answer
76 views

Quantum map and preservation of trace

I am currently learning about quantum maps, ie maps that transform a density matrix into another one. Assume we are in the Hilbert space : $H_A \otimes H_B$. I call the quantum map on the density ...
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How is Anderson Localization a quantum-mechanical phenomenon? How to compare it with classical case? [duplicate]

I was reading book of 50 Years of Anderson localization, which mentions that it highlights wave particle duality. What does it mean? About this localization I have also read that we can understand it ...
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1answer
36 views

Translation operator in polar coordinates

Accordingly to Stone's theorem the generator of a strongly continuous one-parameter unitary group is self-adjoint. The translation operator in the radial direction in Cartesian coordinates is ...
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1answer
44 views

Can an electron absorb a photon even if it exceeds the energy required for the electron to jump up an energy level?

To clarify my question, consider the hydrogen atom. An electron on the ground state needs 10.2 eV to be excited to the second state (first excited state). If a photon with less than 10.2 eV strikes ...
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1answer
41 views

How to relate random matrix theory with Quantum mechanics approach

In Quantum mechanics we first built Hamiltonian and then find its eigenvalues and eigenvectors. How I can relate this with random matrix theory?
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56 views

Derivation of quantum scattering of 1D square well

The above is the question. In my book, I'm given this formula for calculating the transmission probability (when E>V_nought): Here, k1 = sqrt(2m(E-V_0))/h_bar However, the problem is that this ...
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2answers
56 views

Definition of the spherical harmonics do not agree

I Griffiths' Introduction to quantum mechanics, the spherical harmonics are defined as $$Y_l^m(\theta,\phi) = \epsilon\sqrt{\frac{2l+1}{4\pi} \frac{(l-|m|)!}{(l+|m|)!}}e^{im\phi} P_l^m(\cos \theta)$$ ...
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2answers
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Why position and momentum operators are both continuous spectrum while angular momentum is discrete? [duplicate]

We know that position $\hat{r}$ and momentum $\hat{p}$ are both continuous spectrum operators, i.e. $$\hat{r}|r'\rangle=r'|r'\rangle, \quad \hat{p}|p'\rangle=p'|p'\rangle.$$ But the angular operator $\...
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1answer
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How do we know which term to attach a phase factor to in a state equation?

I need to find the state of a particle in a one-dimesional harmonic oscillator where a measurement of the energy yields the values $\hbar\omega\over 2$ or $3\omega\hbar\over 2$, each with a ...
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1answer
42 views

Meaning of units in the Heisenberg Uncertainty Principle

So we have the inequality $\Delta x\,\Delta p\geq \hbar/2$ Why is the uncertainty of position in meters? Isn't uncertainty measured in probabiliies? Does it make sense to say that the uncertainty in ...