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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What is the cellular automaton interpretation of quantum mechanics?

Gerard 't Hooft has presented a new interpretation of quantum mechanics called: Cellular Automaton Is there anyone who can give a summary of the main points of the interpretation and its main ...
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What is the role of an observer in "consciousness causes collapse"? [duplicate]

If a "conscious observer" is part of a theory of physics (e.g. some versions of QM, cosmology), then how (according to what theories) did the universe evolve before the existence of ...
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Measurement Problem Explained by Interaction of Operator With Adjoint Having Larger Domain?

Quantum physics axiomatically uses a self-adjoint operator for a measurement. In general, the adjoint of an operator has a larger domain than an operator. Could it be that the "measurement ...
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What is a good way to represent spin state in a 2D graphic when phase is undefined?

If a spin state is fully defined each complex number can be plotted on a 2D graph with a label on each point like the two spin states plotted here: However, in the applet I'm trying to create, phase ...
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How does chiral symmetry breaking generate most of the mass for baryons?

So I know that chiral symmetry is a part of the $SU(3)$ group and under SSB, it can generate most of the baryons' mass that doesn't come from the quarks' rest mass. However, I am not so sure and ...
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Troubling with the application of Fourier series on this wave function [closed]

@5:00- 5:26 in the youtube vdo linked below, a square wave function is discontinued at -piR and piR (first pic). To apply Fourier series, we can demand that the wave function repeats itself and is ...
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Meaning of rotational invariance breaking and lifting of degeneracy

The $2p$ level of hydrogenic atoms are $3-$fold degenerate. That is $\psi_{210}$ and $\psi_{21\pm1}$ all have the same energy $E_{n=2}$. And the level $n=2$ as a whole is $4-$fold degenerate, since $...
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A possible link between General Relativity to Quantum Theory? [closed]

So, I want to begin by talking about the bouncing oil droplet experiment which shows that a droplet displays similar behaviors as quantum particles as it bounces in an oil bath under a low-frequency ...
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Why is the wave function of a particle with definite momentum $p$ given as $e^{ipx/\hbar}$?

In many textbooks it is stated that, in position space, the wave function of a particle with definite momentum $p$ is given by $e^{ipx/\hbar}$. I know that the $\hbar$ comes from the de Broglie ...
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Step between the commutation of $[H_e, x]$ from $2p$ to $1s$ transition [closed]

so i am evaluating the matrix elements for 1s to 2p as shown in the picture below. I just don't understand the last step on how [$[H_e, x]$ evaluates to $E_{1s}$ to $E{_2p}$ as shown in highlighted ...
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One-dimensional Kohn-Sham equation solution [closed]

I wish to make a problem related to the Kohn-Sham equation in a self-consistent manner. Solvers are supposed to be able to write simple codes with using Python or Julia. To simplify, I limit myself to ...
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Time evolution operator in the Heisenberg picture [closed]

For an operator $A$, we can show that $\langle A_H \rangle = \langle A_{S} \rangle$, since $$\langle \Psi_S(t)| A_S|\Psi_S(t)\rangle = \langle \Psi_S(0)| U^{\dagger}A_S U|\Psi_S(0)\rangle$$ $$U^{\...
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Why are the undersides of clouds (which are made of transparent water droplets or ice crystals) dark?

I have read this question: High-scattering barriers are opaque for the same reasons that the undersides of clouds (which are made of transparent water droplets or ice crystals) are dark. There is ...
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2 answers
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Exciton-phonon coupling Hamiltonian

I'm reading this article about coherent exciton transport in photosynthetic light harvesting and the role of quantized vibrations. Along the way, I came across a section where the article claimed the ...
2 votes
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Local symplectic transformations on Gaussian states

According to Eqn. $(18)$ of this paper, given a two mode Gaussian state with the $4 \times 4$ covariance matrix $\sigma$, it is possible to find a symplectic matrix $S = S_1 \oplus S_2$, where $S_{1, ...
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Cite a real-world experiment that induced entanglement [closed]

I'm a quantum mechanics newbie but I have some background in more "macro" experimental sciences such as biology and psychology. I'm also well-versed in probability theory, so I have no ...
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Electron localization in crystal

I tried to use indetermination principle to explain why, electrons that are strongly bounded to the nucleus, are more localized. Unfortunately, the result that I've obtained says the exact opposite. ...
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How to evaluate the commutation relations in the Heisenberg equation of motion (Polarisation)

For a Hamiltonian in the following second quantisation form:\begin{equation} H=\begin{aligned} & \sum_{\vec{k}, s} E_{c, s}(\vec{k}) c_s^{\dagger}(\vec{k}) c_s(\vec{k})+\sum_{\vec{k}, s} E_{v, s}(\...
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Probability in superposition of states [closed]

Suppose that we have a machine which contains a particle $P$ and a system $S$. The particle is in the state $\frac{1}{\sqrt2}(|\uparrow\rangle + |\downarrow\rangle)$. The system $S$ has three possible ...
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Ramsey Interferometry in Three-Level Anharmonic System

Recently I've been studying the pulse-level control experiments available in Qiskit like the $T_2$ Ramsey experiments. I came across this page and was surprised to find that there are three- and even ...
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The number of particle for an idea bose gas [closed]

Consider an ideal gas of bosons whose density of states is given by for some constants and . Derive an expression for the critical temperature , below which the gas exp
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Is rigged Hilbert space generally considered the correct structure for QM?

I am currently reading the quantum mechanics text by Ballentine and, over and over, arguments are made (e.g. Chapter 4.6 on constraining the wavevectors of free particles to be real) which rely on ...
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What is the effect of magnetic field on PHASE of instrinsic spin of fermion?

As part of my bucket list of things to understand before I die, I'm looking at and trying to understand variations of the Stern-Gerlach experiment. (I haven't studied physics since I was at school and ...
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Why isn't velocity operator given as $\mathbf v=\mathbf {\frac{d\hat R}{dt}}$ [duplicate]

Cohen-Tannoudji pp 223 The observable $\mathbf A$ which describes a classically defined physical quantity $\mathscr A$ is obtained by replacing, in the suitably symmetrized expression for $\mathscr ...
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Why do we only look at transitions between energy-eigenstates, when perturbing a system with an oscillating interaction?

I have some doubts about the usual explanation of sharply peaked emission / absorption spectra, that one can observe when one looks at quantum mechanical systems, for example the hydrogen atom. In ...
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State transition (continuum)

If we assume that because of factors, a quantum mechanical system needs to rearrange itself, and in doing so, it might change it's state, to another one. In our consideration, we tried to find the ...
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Does light attract charge? [duplicate]

Light is an electromagnetic wave, with an electromagnetic field. Does it attract/repel charge?
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Averaging transition rate for absorption in dipole approximation for unpolarised radiation

The transition rate corresponding to the first-order probability of absorption is given in the dipole approximation as $$W_{ba}=\frac{dP_{ba}^{(1)}}{dt}=\frac{\pi I(\omega_{ba})}{\hbar^2 c \...
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Heisenberg Picture unclarities

In our lecture about this topic, the two following statements were made: An Operator $O_S$ (Schroedinger Picture) can be time dependent. But only when the operator $O_S$ is time independent, the ...
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1 answer
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Expressing a state in Schröndinger picture and time evolution operator

I have two question, regarding the derivation of two expression that I will post below: If we have $\{ |\phi_{n,\tau}\rangle\}$ the set of eigenvectors of the Hamiltonian of a system. This set, is at ...
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Connecting asymptotic scattering solutions to short-distance numerical potentials

Problem I'm dealing with a one dimensional quantum mechanical scattering problem in a finite region, say $x\in\left[0,L\right]$. At first, this problem is defined as a finite-difference problem, i.e., ...
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Harmonic perturbation in interaction of radiation with quantum system; making sense of approximation of the integral

In the chapter "The interaction of quantum systems with radiation" (Quantum physics book by Bransden and Joachain, 2nd edition) section 11.2 "Perturbation Theory for harmonic ...
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Boson self-energy in the presence of cubic terms

I am somewhat new to many-body theory, and I would like to calculate the spectral function for a system of interacting phonons. The boson Hamiltonian takes the form $H = H_2 + H_3 + H_4$, with $$H_2 = ...
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How can we detect gravity phase-shift in quantum mechanics?

I have been searching for a satisfying answer on how we can detect the predicted phase shift due to the gravitational potential in quantum mechanics. Specifically, Sakurai, describes in his book the &...
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1 answer
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What happens to the normalization condition if the wave function is non stationary?

The quantum mechanics courses I have taken as of now pretty much only deal with stationary states of the form: $$\psi(x,t) = \psi(x)\exp{\left(-\frac{iE}{\hbar}t\right)} $$ Now, what about situations ...
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1 answer
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Is this operator Hermitian? Commutator of non-Hermitian operators [closed]

In the derivation of a Master Equation, I am left with two additional terms: $$ \sigma_j [\sigma^{\dagger}_k,\rho] - [\rho, \sigma_k]\sigma_j^{\dagger} \quad ,$$ where $\sigma_j = |g\rangle \langle e|...
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Ising configuration after rotation in one sub-lattice

I do not understand Eq. (5.9) in Auerbach's book Interacting electrons an quantum magnetism. Consider the general spin-$S$ Heisenberg model on a bipartite lattice with $N$ sites: $$ H = \frac{1}{2} \...
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Doubt about definition of creation operator

I am a past physics student and wanted to revise the rudiments of many body theory, in particular as related to materials physics. I have a doubt about the definition of creation and annihilation ...
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Operators localized in space and $\hat{q}$ position operator

I am reading the "Quantum Field Theory lectures of Sidney Coleman". In the first chapter (subchapter 1.2), the author talks about translation invariance. In particular, he states that $U(a)=...
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The many-worlds interpretation and a free particle

How does the many-worlds interpretation understand the time evolution and spread of a free particle wave function? That is, does every continuously small change constitute a cosmic action that causes ...
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Degeneracy of ground state of periodic AKLT model

I have a question regarding the degeneracy of the ground state of AKLT Hamiltonian. Periodic AKLT Hamiltonian is known to have a unique ground state which can be written as a matrix product state (...
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Two particles in a potential well [closed]

I happen to be very new to quantum mechanics, and I am self-teaching myself through the Griffiths textbook. I was hoping to get clarification on the following problem: Consider two noninteracting ...
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Do i need to learn classical physics before start learning quantum mechanics [closed]

I'm a medical student I'm in the 2nd year of my course. I am curious about quantum physics and want to learn, it's been roughly 3 years since i left maths(I was very good at maths) and i know very ...
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1 answer
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Relationship between wavelength and storage

I have a question regarding the working of optical discs. We know that Blu-ray disc stores more data than DVD. There are two reasons for that: The pits are smaller The wavelength of blue light is ...
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WKB approximation derivation for $E<V$

I understand that we can write any complex wavefunction on polar form $A\exp(iθ)$ with both $A,θ$ real. Following the logic of Griffiths on WKB (here, page 291): We write the energy wavefunction in ...
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Is quantum physics true? [closed]

Well, as I was researching about quantum physics, there was an point that “if there is not any observer the object is in wave form and the moment when an observer watch comes it coverts into an sold ...
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Decoherence via environmental photons

I am reading the book "Decoherence and the Quantum-to-Classical Transition" by Maximilian A. Schlosshauer, and I have come to understand that for a two-level system with eigenstates $|a\...
3 votes
1 answer
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Can we think of spontaneous emission of a photon from an excited atom as a driven harmonic oscillator problem?

This is a kind of strange question, but I'm wondering, in the context of a fully quantum field theoretic treatment of spontaneous emission, if there is any model or way of calculating the process that ...
1 vote
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KLEIN Paradox phenomena

We considered the case of a relativistic fermionic particle in a potential well. We divided the region in two zones, the one where the potential is zero and the one where it has a values $V_0$. The ...
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Quantum angular momentum addition of two particles

I am learning about the angular momentum addition rule. we have two particles, both with s=1/2 and L=0, and we need to find the total J of the system. We know that J = J1+J2, J1-J2, so in our case J=...
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