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-theory tag for the theory of many-body quantum-mechanical systems.

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31 views

Interaction (Dirac) picture and time dependent perturbation theory

Why in many, if not all, references that discuss the time dependent perturbation theory, they start the discussion with the interaction (Dirac) picture, although, what we need is only solving the time ...
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1answer
59 views

Quantum mechanical reasoning to seeing colours

I don't know if I am writing but this is how I understand it: If I am looking at blue paint... White light falls onto the paint, the electron in the atoms of the paint absorbs all white light and ...
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4answers
171 views

Is wave function collapse non-local or local?

Imagine a particle in a very large box which takes years to travel from one end to the other. Alice and Bob are outside the box, on opposing ends. Each can remove their side of the box to check if the ...
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1answer
38 views

Instantons as classical solutions

Instantons are classical solutions of the Euclidean (i.e. imaginary time) classical equations of motion. The standard example from single particle 1D QM is taking a potential of the form $V(x)=(x^2-a^...
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Expectation values of operators that do not correspond to an observable [closed]

The ground state of BCS state is $$|\Psi_{BCS}>\ =\ \prod_{\vec{P}}(u_{\vec{P}}\ +\ v_{\vec{P}}b_{\vec{P}}^{\dagger})|0>$$ What is the expectation value of the creation operator <$b_{\vec{P}}...
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Is it a typo in David Tong's derivation of spin-orbit interaction?

A few lines below equation 7.8 D. Tong writes The final fact is the Lorentz transformation of the electric field: as electron moving with velocity $\vec{v}$ in an electric field E will experience a ...
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1answer
124 views
+150

The Spin Term of the Angular Momentum Tensor in Relativistic Quantum Mechanics

In Relativistic Quantum Mechanics, an Angular Momentum Tensor is defined ($J_{\nu \mu}$). This tensor is divided into two terms, one responsible for the spin angular momentum ($S_{\nu \mu}$) and one ...
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31 views

Fermi’s golden rule integral over energy states, time constraints

In perturbation theory, we can, to first-order, arrive at an expression for transition rates that looks like $$ \Gamma = \frac{2}{\hbar} |M_{if}|^2 \frac{\sin{\frac{E_f-E_i}{\hbar} t}}{E_f-E_i}. $$ ...
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2answers
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Band structure of a nanoparticle

Considering a crystal at such a small size (for example, a sphere with diameter about 20 atoms) that the periodic boundary condition assumed in Bloch Theorem is not really a good estimation, I wonder ...
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40 views

Two-level system + bosonic field: an arbitrary choice of operators ordering leads to two different results

I encountered a situation where two seemingly equivalent choices of the ordering of operators lead, after some calculation, to two non-equivalent operator orderings. Consider the interaction between ...
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What is the Schrodinger equation of $n$th spin particle? [closed]

I get those equations from this https://readingfeynman.org/tag/schrodingers-equation-for-spin-1-particles/ The schrodinger equation for spin zero particle like pion $$i\hbar\frac{\partial \psi}{\...
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Proving the Equal-time commutation relations if Schrodinger Fields [closed]

The Schrodinger fields can be represented as How we can prove the the commutation relations between psi and psi *? Also how could we write the expression of hamiltonian H and the total number ...
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1answer
44 views

Simplest tight binding

My lecturer is teaching the Bloch theorem, which I saw many years ago in Griffiths textbook on Quantum mechanics. I cannot recognise it in the form that my lecturer is using. We are studying a tight-...
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1answer
31 views

Generalised measurements and collapse

My reference is Nielsen and Chuang's "Quantum Computation and Quantum Information". When introducing qubits, $|\psi\rangle=\alpha|0\rangle+\beta|1\rangle$ the authors state that (*)When we measure ...
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1answer
21 views

Labeling the eigenstates of the many electron Hamiltonian

I'm taking a course on atomic and molecular physics and there is a chapter about finding suitable quantum numbers that label the eigenstates of a given Hamiltonian. The lecture notes say that it ...
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Terminology for photoelectric effect

I'm currently writing a report on the photoelectric effect and I can't figure out how to say what I want to say. Essentially, I want to describe it as a "binary system" or "on/off system" (in that ...
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2answers
68 views

Quantum entanglement and information transfer faster than light

According to quantum entanglement theory, if the spins of two particles are in superposition and then spin of one particle is observed, the spin of the other particle is determined immediately. While ...
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15 views

Bit threads as noisy quantum channels

In literature on the holographic duality, recently a new way of looking at the Ryu-Takayanagi formula has been presented, where the minimal surface area has been replaced by the maximum number of "bit-...
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1answer
42 views

When do quantum mechanics effects become important in this case?

Consider a free electrton with energy E in a metal. At which energy do the quantum mechanics effects become important? When should I consider the electron as a wave and not as a particle? I thought ...
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1answer
56 views

Why $Q|0\rangle=0$ where $Q$ generates a symmetry?

Quote: "Concepts of Elementary Particle Physics" by Michael E. Peskin In quantum mechanics with a finite number of coordinates, it can be shown that, if $Q$ generates a symmetry of the theory, then ...
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1answer
45 views

Decoherence Tutorial on level of the Theoretical Minimum books

I'm trying to understand decoherence and other issues in QM related to the Everettian interpretation. I have a BS in physics, but that was 37 years ago. I've read Susskind and Friedman's book, The ...
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Calculating Spherical Harmonic Expansion Coefficients [closed]

I showed my professor my work but she got .624 for $c_{00}$. I know that $\int_{\pi}^{\pi/2}0d\theta=0$, so I should just be left with $\int_0^{\pi/2}Y_0^0\psi(\theta,\phi)sin(\theta)d\theta d\phi$. I ...
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1answer
55 views

Why doesn't the sunlight supersede the effects of the bodies of water and the ground on the temperature of the atmosphere?

I am not asking about why the summer is hotter then the spring. I do understand that the body of water on the surface of Earth needs to cool off and warm up, and that takes more time then for the ...
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2answers
33 views

Addition of two angular momenta

In addition of angular momenta, does both the relations depict the same thing? $$ \vec{J} = (\vec{J_1}\otimes 1 +1\otimes \vec{J_2}) $$ $$ \vec{J} = (\vec{J_2}\otimes 1 +1\otimes \vec{J_1}) $$
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1answer
48 views

Wigner-Weyl transformation for particle in magnetic field

I consider particle in external magnetic field, ${\bf A}=(-yB,0,0)$ and find wave functions (may be up to normalization factors), $$\psi(x,y,z)=\sum_n\sum_s\int\frac{dp_xdp_z}{(2\pi)^2}f_s\left(eBy+...
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16 views

Bond distance change on ionization

The bond distance increases on ionization for the molecules C2 and N2, but decreases for O2 and F2. As far as I know, the bond should get longer when the amount of electrons involved decreases (which ...
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2answers
86 views

About the boundary conditions in the finite potential wall

Suppose we have a finite potential wall with a "depth" $V=-V_0$ and a radius of $a=1.5$ fm. The exercise now states that $\Psi(r) = u_0R(r) = u_0\frac{u(r)}{r}$, where $$u(r) = \begin{cases} A\cdot \...
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1answer
48 views

Solving a two variable integration [closed]

I was going through the solid state book by Philip Phillips. I came across an integral similar to: $$\int_{0}^{\beta}d\tau d\tau^{'}e^{-E_c|\tau-\tau^{'}|}$$ where $\beta E_c >> 1$. I am not ...
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Difference between multiphoton signal and, $n$-photon signal state

I was reading decoy state quantum key distribution article, by Lo et.al. (PRL paper , PRA paper). In this article, authors have discussed the possibility of photon number splitting attack due to ...
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2answers
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Why is the blackbody emission spectrum independent of what frequencies are absorbed?

So a blackbody absorbs all incoming radiation and at thermal equilibrium emits radiation according to Planck's law. I have several questions. How could blackbody absorb all incoming radiations? In ...
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Coupled Quantum Harmonic Oscillator Question HELP! [closed]

hello i need help solving this review excursive questions plea help abdi
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1answer
69 views

Electrons can't orbit at any old radius [closed]

Electrons can't orbit at any old radius from the atom's nucleus, but are rather restricted to only specific orbits at a fixed set of distances. This is called orbital quantization. Why this ...
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Is $\int f(x) |x \rangle\langle x| dx = \int f(x) dx$?

If not how would it be evaluated? I'm guessing as above based on the idea each $|x_0\rangle\langle x_0|$ "component" will equal 1 so we will be left with just $f(x_0)$ in the integrand - which we ...
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34 views

Proof for $p$ and $q$ eigenstates using only commutation relations [duplicate]

I should proof that $$p \langle q;t\lvert p;t \rangle = \frac{1}{i}\frac{\partial}{\partial q} \langle q;t\lvert p;t \rangle $$ using ONLY the commutation relations and the fact that $q$ and $p$ ...
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1answer
14 views

Squeezed state expectation value form

What is the form of $$S^+px^2S$$? (where $S$ is the squeeze operator.) I know the form of $S^+pS$ and $S^+x^2S$ but no matter how I calculate it I cant find the form for $S^+px^2S$. The main problem ...
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1answer
67 views

According to quantum uncertainty, can an object transform into another object even with extremely low probability?

First of all I would like to point out that when it comes to quantum physics, I have very poor knowledge so please excuse me if I misuse some words to describe what I mean. My question is based on ...
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20 views

Is the Fock state the only state corresponding to the n particle wave function?

The n particle wave function corresponds to the n particle state called Fock state. Is this Fock state the only state associated with the wave function? Is the Fock state defined artifitially? Can ...
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1answer
73 views

Quantum Mechanics Spectral theorem proof [closed]

Has anyone an idea how to prove the spectral theorem $A = \sum_{i} \lambda_i P_{\lambda_{i}}$. Starting from $A|\Psi_{i}\rangle=\lambda_{i}|\Psi_{i}\rangle$ or what ever?
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Quantising classical harmonic oscillator like classical fields

Iam studying QFT, But Iam stucked at catching the mathematical formulae for harmonic oscillator analogue in QFT, For a classical harmonic oscillator I can write $x(t)= Ae^{i\omega t} +A^{\dagger} ...
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1answer
95 views

Path integral for non-standard Hamiltonian $\hat{H}=\hat{x}\hat{p}^2\hat{x}$

Given the Hamiltonian $\hat{H}=\hat{x}\hat{p}^2\hat{x}$ with position operator $\hat{x}$ and momentum operator $\hat{p}$, I should give an explicit expression for the measure of the path integral, $$ \...
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29 views

Do basis transformations of fields in QFT need to be unitary?

I know that it is possible to diagonalise kinetic terms in a QFT Lagrangian using generally non-unitary matrices to transform fields. For example https://physics.stackexchange.com/a/377299/91934. ...
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Restriction master equation to single-particle subspace

In Anastopoulos and Hu - A Master Equation for Gravitational Decoherence: Probing the Textures of Spacetime (https://arxiv.org/abs/1305.5231), they restrict the system to a single particle subspace (p....
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1answer
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Instant communication of heavy body

A transmitter projects a powerful photon beam which forms a (probability) cone. An instrument measures the direction of the force exerted by the transmitter. When a large mass such as a black hole ...
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68 views

Understanding the meaning of “Orders” in Perturbation Theory in Quantum Mechanics

While learning time-independent perturbation theory, there was something that I couldn't understand, and it has to do something with order of $\lambda\\$ For example, when deriving the equation for ...
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1answer
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If a basis set is complete, are the elements in it mutually orthonormal?

If a basis set is complete, are the elements in it mutually orthonormal? For example, we can express the field operator in the basis of the creation and annihilation operators.This basis is complete, ...
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Relation between irreducible representations and eigenstates

When in quantum mechanics the Hamiltonian possesses some symmetry, then knowing the irreducible representations of the group to which the symmetry belongs gives information about the eigenstates. As ...
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1answer
62 views

Solving a differential equation using factorisation

In Griffiths Introduction to Quantum Mechanics, when discussing ladder operators in Chapter 2, he write Schrodinger's equation as, $$ \frac{1}{2m}\left[\left(\frac{\hbar}{\mathrm i}\,\frac{\mathrm d}{\...
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+50

Hybrid orbitals, photoionization and time dependence

Wikipedia, in the article on Orbital Hybridisation, states the following: One misconception concerning orbital hybridisation is that it incorrectly predicts the ultraviolet photoelectron spectra of ...
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1answer
129 views

How we can measure speed with time, when the rate at which time passes depends on speed?

I was thinking about relativity, specifically about how we travel at the speed of light in 4 dimensions. The higher one’s velocity in space, the lower one’s velocity in time. Inversely, the lower one’...
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1answer
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What does the density of states of a bulk material, 2DEG, quantum wire and quantum dot tell me?

This is a rather long winded questions so I hope that I can get my questions across as coherent as possible. Background: I am a third Semester Nanoscience student and I am taking my first QM course ...