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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90 views

A common misunderstanding regarding which path information in a double slit and Mach-Zehnder interferometer?

I just can't get my head around this. What does he mean when he says that a hit at one of the detectors doesn't imply that the particle went though a certain path? He calls this the "separation ...
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18 views

Double-slit experiment: particle sizes / properties? [duplicate]

I only have very limited knowledge and understanding of quantum mechanics, and you might know that, for topics one has no expertise in even trivial information is buried underneath thick layers of a ...
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26 views

How does reflection work at a quantum level? [duplicate]

Thinking of light in corpuscular form, how does the bouncing of a photon off a reflective surface work? Is it the same photon bouncing off, or is it absorbed and re-emitted? If it's bouncing, does it ...
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26 views

The arithmetic product of quantum spins as a linear operator

I am reading Quantum Mechanics The Theoretical Minimum by Susskind and Friedman. The authors set up a two spin system and two observables $\sigma_z$ and $\tau_z$ that measure the spin of of ...
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1answer
58 views

How to show that translational invariance in $y$ of implies that it's an eigenstate of $p_y$?

Let us consider a particle on a plane with uniform magnetic field $B=B\hat{z}$, and hence with the Hamiltonian $H=\frac{1}{2m}(\vec{p}+e\vec{A})^2$. I am concerned with finding the energy eigenstates, ...
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1answer
36 views

Stinespring dilation of a channel vs Naimark's theorem

I'm trying to understand the connection between the Stinespring dilation of a quantum channel and Naimark's theorem that shows that POVMs can be written as projective measurements in a larger Hilbert ...
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4answers
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Does $U^T U$ have real eigenvectors if $U$ is unitary?

I was reading a paper by Kraus and Cirac on general two qubit gates. A crucial step is to decompose an arbitrary unitary operator acting on two qubit space into a special form: $$ U_{AB} = U_A\otimes ...
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1answer
89 views

How to read bra-ket notation? [closed]

Good afternoon, I am trying to understand the basics of some quantum mechanics theorems (e.g. Uncertainity principle). I'm looking for the correct way to read this expression while I'm speaking. For ...
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1answer
62 views

Energy release/gain in superposition (in Stern-Gerlach)

Let's have a quantum system in superpositon of two states $|e>$ and |g> with coefficients a and b. Now the system interracts with a field and is projected on either |e> or|g>. The question is what ...
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1answer
69 views

Is there an integral form of the equations of QM or GR?

Maxwells equations and also the equations of fluid dynamics can be formulated as integral equations. These equations allow so called weak (non-differentiable) solutions, e.g. shock waves in fluid ...
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Correct form of Uncertainty Principle [duplicate]

In a book of mine, the author wrote that $$\Delta x \Delta p_x \geq h$$ However the usual form of the Uncertainty Principle I saw in many places is $$\Delta x \Delta p_x \geq \frac{h}{4\pi}$$ So I ...
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1answer
42 views

Which matrices represent unitary projective representations of ${\rm SO(3)}$?

I was reading this post which triggered the following question. The group ${\rm SO(3)}$ is real orthogonal. However, it is possible to consider representations of ${\rm SO(3)}$ on a complex vector ...
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2answers
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Is there a connection between the spreading of the wave packet of the universe and the time arrow?

Entropy of position and wave packet spreading. Why do wave packets spread out over time? Wave packet of the universe and its  spreading. Is there a connection between the spreading of the wave ...
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First-order correction to wave function in time-independent perturbation theory

In time-independent perturbation theory, while considering the first order correction to wave function, it can be written as linear combination of the unperturbed states except its own unperturbed ...
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38 views

Books for self-learning theoretical physics mostly related to Quantum physics and Relativity [duplicate]

I am self-learning theoretical physics, and I've just finished my first book: Physics for Scientists and Engineers 8th Edition by Serway and Jewett. I want to know what books should I read next, and ...
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1answer
33 views

Physical meaning of whole state space for spin-one

The spin-one quantum states belong to $\mathbb{C}^3$, with a set of orthonormal bases taken as the spin component along a direction, which would correspond to the direction of the magnetic fild ...
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Will 1s electron in element with z greater than 137 have an imaginary energy? [duplicate]

If we consider energy in terms of rest mass E=Mc^2 for an electron where M is the rest mass and c is the speed of light then does the 1s electron of an element with z>137 have an imaginary energy?
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1answer
54 views

Is this interpretation of the Copenhagen Interpretation accurate in this book from Bruce Rosenblum and Fred Kuttner?

I'm very new on this particular subject, can anyone help me determine how accurate the interpretation of Bohr's quote is, and where is the origin of this quote?
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81 views

What is the quantum mechanical turning point of the $n^{th}$ energy eigenstate of an oscillator? [closed]

I am looking for an analytical expression for the most likely position for a quantum harmonic oscillator (which I refer to as the quantum mechanical "turning points"), in terms of $n$. For the quantum ...
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1answer
83 views

Linearity of Schrödinger equation and perturbation theory

So, I was studying quantum mechanics and reached the point where perturbation theory is discussed. It is my first time in this topic, and something called my attention: it was said that we need ...
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6answers
239 views

How many quantum mechanisms are there to create Light?

I know light is created when an electron moves to a lower energy orbital in an atom. Is this original source of all light we see (sun / light bulbs / fire) or is there another way to produce light ...
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Derivation of the formula for the energy of quantum harmonic oscillator [duplicate]

Can anyone please show how this formula for the energy of quantum harmonic oscillator is derived? $$\epsilon ={\frac {h\nu }{2}}+{\frac {h\nu }{e^{h\nu /kT}-1}}$$
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1answer
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Analogies between equations [on hold]

What properties of fields and matter are related to the analogy of the Schrödinger equation and the Navier-Stokes equation, between the equation of general relativity and the Navier-Stokes equation. I ...
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37 views

One-dimensional Schrödinger equation: reproducing a given set of energy values [duplicate]

Given a set of $N$ increasing real numbers $\{E_1, E_n, \cdots, E_N \}$, is it always possible to find a potential $V(x)$ such that the set of $\{E_j\}$ are the lowest eigenvalues of the corresponding ...
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1answer
35 views

Fermion parity operator

Fermion parity operator is defined as $$ \hat{\mathcal{Q}}=\exp(i\pi\sum_j \hat{n}_j) = (-1)^{\sum_j \hat{n}_j} $$ And also if $\sum_j \hat{n}_j = \sum_j c^{\dagger}_{j}c_j=N $ is constant then it ...
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1answer
48 views

How Creation and Annihilation operator transform under an unitary transformation?

\begin{align} \hat{\mathcal H}= \sum_{i,j} \hat{\psi}^{\dagger}_i H_{i,j}\hat{\psi}_j \end{align} The $\mathcal H$ is the full second quantized Hamiltonian for a system and $H$ is the single particle ...
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1answer
89 views

Clarification for the formulae for Differential Cross Section in Scattering theory [duplicate]

I am trying to study scattering theory using "Quantum Mechanics Concepts and Applications" by "Nouredine Zettili" . He starts from the formula $${d \sigma( \theta,\phi) \over d \Omega } = {1 \over ...
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26 views

Simultanious eigenstate of Hubbard Hamiltonian and Spin operator in two-site model

Known fact If two operators $A$ and $B$ commute, $[A,B]=0$, they have simultaneous eigenstates. That means $A|a,b\rangle=a|a,b\rangle$ and $B|a,b\rangle=b|a,b\rangle$. Hubbard Hamiltonian $H_\text{...
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What caused the first measurement to the universe?

I've been bumbling with a question recently. People postulate that with the give model of big ban, particles forms and breaks and eventually became what we saw as of today. However, if we put ...
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24 views

Conditions for zero mode edge state to appear

Consider a non-interacting translationally invariant system described by H(k), k is the crystal momentum. The dimensionality of the system is denoted as d. I was thinking about what are the general ...
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2answers
69 views

Two-photon interference inside Mach-Zehnder interferometer

Imagine there's a strong laser beam, not just an attenuated stream of single photons, entering a balanced Mach-Zehnder interferometer. One-photon picture: Each photon interferes with itself on the ...
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How to perform a basis change for a matrix product state?

I want to do a measurement on a random direction in each of the individual spins. So if my wave function is represented as a Matrix Product State, can I perform the rotation individually on each ...
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48 views

Mean square values of vacuum fluctuations of the radiation field

It is well known that the mean square values of the electric and magnetic fields of vacuum fluctuations is given by(Welton, Phys.Rev.74, 1157) $${\langle {E^2}\rangle _{Av}}={\langle {B^2}\rangle _{...
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2answers
59 views

Bose-Einstein condensation: Bogoliubov Approximation

I'm trying to understand the Bogoliubov approximation from "Statistical Mechanics" by Pathria and Beale. First of all they say Since $a_0^{\dagger}a_0=n_0=O(N)$ and $(a_0a_0^{\dagger}-a_0^{\dagger}...
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3answers
170 views

Are all processes time/CPT-reversible, e.g. measurement, stimulated emission, state preparation, Big Bang?

"The CPT theorem says that CPT symmetry holds for all physical phenomena, or more precisely, that any Lorentz invariant local quantum field theory with a Hermitian Hamiltonian must have CPT symmetry." ...
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Question about correspondence principle

This question is about a paragraph in Stephen Gasiorowicz's Quantum Physics 3rd edition. The paragraph reads something like this: On the other hand, the frequency of the radiation associated with ...
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1answer
148 views

General wave function equates to one after equating Euler's identity. Why?

Am typing on my phone, so apologies for any mistakes. Basically we know a general wave function taken as an example to be $\psi = e^{i(kx-\omega t)}$ where $k=2\pi/\lambda$ and $\omega=2\pi f$. Euler'...
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1answer
44 views

Level statistics of many body localization

I was calculating some Hamiltonian's spectrum statistics. Namely, I calculated the Hamiltonian's eigenvalues and sorted them in an ascending order: $E_1,E_2,E_3...E_N$. The quantity I calculated is r, ...
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88 views

The frame of truncated momentum basis on a 1D lattice

$\def\ket#1{\left|#1\right\rangle } \def\bra#1{\left\langle #1\right|}$ (This is part of a research problem) The Setup: Consider a single particle on a finite 1D lattice with the Hilbert space ...
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1answer
61 views

Could Schrödinger's universes have different fundamental laws?

It seems that Erwin Schrödinger was one of the first proponents of a multiverse concept. In Dublin in 1952, Erwin Schrödinger gave a lecture in which he said that when his equations seemed to ...
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1answer
125 views

Gauge transformation for Bloch waves?

I have seen in many places saying a gauge transformation transform the Bloch wave function as $\psi_{nk}\to e^{-i\phi_n(k)}\psi_{nk}$. However I don't quite understand how it is related to the "gauge ...
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1answer
40 views

What's the intuition for the reflection of a quantum particle at a potential step equal to the particle's energy?

While doing the problem of potential step, I saw that if the energy of the particle is equal to the potential energy of the step, then the wave function is a constant, or to say the probability ...
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2answers
66 views

Movement of free electrons

How can I understand the movement of free electrons in a conductor taking into account the quantam mechanical approach of electrons i.e. uncertainty of position and momentum etc. Does using quantum ...
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0answers
38 views

Forces in the equilibrium state of a molecule

I'm trying to minimize the energies of hydrogen molecule and lithium hydride molecule with the L-BFGS method and HGH pseudopotential, see arXiv:cond-mat/9803286. Hydrogen molecule works fine but ...
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Could Time-Evolution be antiunitary?

There are serveral Arguments for Time-Evolution to be unitary, for example, time-evolution should preserve the norm of each given state (because elseways the probabillity Interpretation would not work)...
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1answer
49 views

Different energy levels in quantum mechanics

I have a doubt regarding energy levels. I saw that translational energy levels are quasi-continuous, rotational energy levels are discrete and vibrational energy levels are more discrete. I want to ...
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48 views

Penrose experiment

I just read about Penrose interpretation theory about the wave function collapse: https://en.wikipedia.org/wiki/Penrose_interpretation, which could be confirmed/infirmed by the following experiment: ...
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3answers
78 views

From second quantization to first quantized Hamiltonian

In second quantization the Hamiltonian can be written as $$ \hat{H} = \sum_{ij} \psi_i^{\dagger} H_{ij} \psi_j = \psi^{\dagger} H\psi $$ Where, $\psi, \psi^{\dagger}$ are the annihilation and creation ...
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2answers
150 views

Heisenberg's uncertainty principle: what is the correct interpretation?

In this video: https://www.youtube.com/watch?v=xsnTrAEiyHg Prof. Walter Lewin showed when a laser beam passes through a very narrow slit the projection of it becomes wider. He claims it is because of ...
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2answers
196 views

If an atom can have only discrete energy values, why it can move on any speed?

Atom, as a quantum system can have only certain energies. Also, energy, specifically kinetic energy depends on velocity, which should mean, that an atom should move only on some strict velocities, and ...