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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About the meaning of quantum numbers [closed]

could someone elaborate the idea of quantum numbers: Azimuthal quantum number (ℓ) Magnetic quantum number (m) Spin quantum number (s) I want to know: their physical meaning and the origin of ...
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Time evolution operator of a periodic Hamiltonian

Suppose we have a Hamiltonian $H(t)$ with periodicity $T$. The time evolution operator in a full period is $$U_1=\cal{T}e^{-i\int_0^T H(t)\mathrm{d}t}$$, where $\cal{T}$ is time ordering operator; ...
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2answers
96 views

How to understand “always create before we annihilate, not the other way around”?

On the book QFT in a Nutshell by A.Zee page 61 writes Always create before we annihilate, not the other way around. —Anonymous But in this Phys.SE question we are doing it the other way ...
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174 views

Why is there $1/2\pi$ in $\int\frac{dp}{2\pi}|p\rangle\langle p|$?

I'm reading Richard MacKenzie's lectures on path integrals and on page 7 he derives the propagator for the free particle as follows: $$ \begin{align} K &= \langle q'|e^{-iHT}|q\rangle \\ &= ...
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1answer
104 views

Can quantum mechanics be formulated without any reference to pictures?

NOTE: in the following with the word "picture" I refer to Schroedinger, Heisenberg, Interaction pictures, i.e. to the way the time-evolution is "distributed" between states and operators. We often ...
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96 views

Hydrogen energy levels and energy-time uncertainty principle

Some hydrogen atom exists in some excited quantum state, and after some time $\Delta t$ it's de-excited, emitting a photon carrying the energy difference. It is claimed that this photon will carry ...
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Detailed Balance for Quantum Master Equations from System Hamiltonians with Degenerate Spectrum

Kossakowski, Andrzej, et al. ("Quantum detailed balance and KMS condition." Communications in Mathematical Physics 57.2 (1977): 97-110) gave a proof that the stationary state of a quantum dynamical ...
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1answer
33 views

Why does an external laser drive only couples certain levels?

I was always wondering how is it that all the quantum optics levels schemes are depicted as if the laser couples only two certain levels with some frequency. For exmaple the standard lambda system ...
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84 views

Linear vs. quadratic dispersion relation

In wave mechanics the dispersion relation between frequency $\omega$ and wave number $k$ is linear: $$\omega_n=c k_n$$ But in quantum mechanics, based on Schrödinger's equation, one can show that we ...
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Flip of polarisation of light

Consider an optical experiment with photons or light pulses. Is there an optical element that acts in the polarisation degree of freedom like the unitary $$ U = \frac 1 {\sqrt 2} \begin{pmatrix} 1 ...
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40 views

A driven quantum harmonic oscillator (DQHO) [closed]

I'm trying to find the dispersion relation for the DQHO with Lagrangian $$ L(q,\dot q,t)=\frac{1}{2}\dot{q}^2-\frac{1}{2}\omega q^2+F(t)q $$ with $F(t)$ being non-zero for $0<t<T$. The ...
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676 views

Mathematical understanding of Quantum Mechanics

Assuming that $\phi(r) = F (\psi(r))$ for some operator $F$ in Quantum Mechanics. Then, in our lecture today, we said that $$\phi(r) = \langle r|F |\psi\rangle = \int_{\mathbb{R}} \langle r |F| r' ...
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1answer
96 views

Mirror that flips polarisation?

Is it possible to build a mirror which not just reflects a photon but also flips its polarisation from horizontal tho vertical (or vice versa)? The reason why I ask is the following: If I put an ...
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33 views

A confusion about the proof of $\hat{p}|x\rangle=i\hbar\frac{\partial}{\partial x}|x\rangle,$ using $[\hat{x},\hat{p}]=i\hbar~?$ [duplicate]

How to prove $$\hat{p}|x\rangle=i\hbar\frac{\partial}{\partial x}|x\rangle,$$ using $$[\hat{x},\hat{p}]=i\hbar~?$$ The question seems to be uncomplete because for any $f(x)$ ...
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1answer
23 views

Constructing matrix for spin in Stern-Gerlach experiment for arbitrary angle

This is a conceptual question about a problem in Sakurai. I understand how to solve the problem, but there's something about it that irks me, and it feels like I'm missing something. In the problem, ...
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2answers
81 views

Classical logic in concern with QM Mathematics

In no way am I a physicist, so please excuse improperly used terms. It is in my understanding that Quantum Physics does not obey Classical Logic, hence the existence of Quantum Logic. My questions ...
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32 views

Finding out time $t$ when a particle is more likely to be on the right half than the left half of the box [closed]

Question: A particle with mass $m$ is trapped in a box of length $L$. At $t=0$, it has wavefunction as following: $$\psi(x,t=0)=\sqrt[]{\frac2{41\pi}}(3u_1(x)+4u_2(x))$$ where $u_1(x)$ and ...
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50 views

Energy Dispersion in Young's Double Slit Experiment

In Young's double slit experiment, when you see the diffraction pattern, why does the intensity of the light fade out as you move from the central maximum? I think it has something to do with the ...
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1answer
59 views

Can the simulation argument be ruled out? [closed]

I am neither a physicist nor a mathematician - simply an interested beholder of the current situation interested in quantum physics and quantum mechanics. So please bear with me regarding any ...
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1answer
78 views

Normalization of a wavefunction that's superposition of two unknown energy eigenfunctions

Question:$$\psi(x)=A(3u_1(x)+4u_2(x))$$where $u_1(x)$ and $u_2(x)$ are energy eigenfunctions. How to normalize function $\psi(x)$? My intuitive solution: I got ...
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1answer
30 views

Introductory Quantum, trouble with this boundary condition and potential

Working on problem 2.40 from Griffiths but can't seem to understand the first boundary condition. We are given the potential $V(x) = \left\{\begin{matrix} \infty & x < 0\\ ...
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41 views

Complexity of a physical system

Are there any accepted definitions quantifying the complexity of: a) macroscopic, classical mechanical systems (e.g., a bicycle) b) microscopic systems (ensembles of atoms)? By the way, I'm not ...
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47 views

Change of Basis For Pauli Matrix From Z Diagonal to X Diagonal Basis

I want to find a matrix such that it takes a spin z ket in the z basis, $$ \lvert S_z + \rangle_z $$ and operates on it, giving me a spin z ket in the x basis, $$ U \lvert S_z + \rangle_z = ...
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Semiclassical limit of Quantum Mechanics

I find myself often puzzled with the different definitions one gives to "semiclassical limits" in the context of quantum mechanics, in other words limits that eventually turn quantum mechanics into ...
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96 views

Motivating Complexification of Lie Algebras?

What is the motivation for complexifying a Lie algebra? In quantum mechanical angular momentum the commutation relations $$[J_x,J_y]=iJ_z, \quad [J_y,J_z] = iJ_x,\quad [J_z,J_x] = iJ_y$$ become, on ...
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Motivating Complexification of Lie Algebras? [duplicate]

What is the motivation for complexifying a Lie algebra? In quantum mechanical angular momentum the commutation relations $$[J_x,J_y]=iJ_z, [J_y,J_z] = iJ_x, [J_z,J_x] = iJ_y$$ become, on ...
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1answer
41 views

A vector function of a vector $\mathbf{S}$ must be given by a multiple of $\mathbf{S}$?

I've been reading Ballentine's Quantum Mechanics, A Modern Development and a statement made in Chapter 3 has been puzzling for me. In Chapter 3 of his book, Ballentine derives the kinematics and ...
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69 views

Rewriting the Hydrogen Schrodinger Equation as a system of differential equations

I have only ever seen the Schrodinger equation for the hydrogen atom written out in a form like this: $$ -\frac{\hbar^2}{2\mu}\left[\frac{1}{r^2}\frac{\partial}{\partial r}\left(r^2\frac{\partial ...
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39 views

Scattering and bound States

So from my understanding, as long as $E>0$ you will have scattering states and these scattering states will always result in an imaginary $\psi$, but bound states can also have an imaginary ...
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75 views

How to prove $\hat{p}|x\rangle=i\hbar\frac{\partial}{\partial x}|x\rangle$,using $[\hat{x},\hat{p}]=i\hbar$? [duplicate]

How to prove $$\hat{p}|x\rangle=i\hbar\frac{\partial}{\partial x}|x\rangle,$$ using $$[\hat{x},\hat{p}]=i\hbar~?$$ The question seems to be uncomplete because for any $f(x)$ ...
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2answers
67 views

Eigenvalues being physical observables

I think I'm comfortable with the PDE solutions to the Schrodinger equation. But as soon as we start putting these values in a matrix (in dirac notation), I lose my understanding and everything ...
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3answers
188 views

Is there an objective, external reality according to quantum physics?

In quantum physics, a particle can be in a superposition of two states until it is measured. In other words, the aforementioned particle doesn't have a definite state until it is "looked at" ...
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2answers
39 views

About completeness relation from discrete to continuous limit

In quantum mechanics, the completeness relation for discrete and continuous basis are $$\begin{align} \sum_n \lvert n \rangle \langle n\rvert &= 1 \tag{1} \\ \int \lvert x \rangle \langle x ...
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35 views

Determining bound states for delta function potential

I'm working on a problem out of Griffith's Intro to QM 2nd Ed. and it's asking to find the bound states for for the potential $V(x)=-\alpha[\delta(x+a)+\delta(x-a)]$ This is what I'm doing so far: ...
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27 views

Could we imagine spin as rotating probability densities (orbitals) in a kind of expanded orbital model?

I know there is no spin in orbital model. And it is always said there is no visualization for the spin. But why not just let the oribtals rotate with 4D quaternions in some 3D dynamic model?
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4answers
108 views

Is this an entangled state?

Is the following state entangled? $\left| \psi \right> = \alpha_0 \beta_0 \left| 00 \right> + \alpha_0 \beta_1 \left| 01 \right> + 0 \left| 10 \right>+ \alpha_1 \beta_1 \left| 11 ...
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51 views

Free will theorem advice [duplicate]

I'm trying to understand the free will theorem which has been constructed by John Conway. Are they saying that particles have free will because they cause their behaviour in response to the ...
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1answer
43 views

Total magnetic moment in an atom

I have a doubt regarding the calculation of total angular momentum of electron in an atom.Which is the right way to do it? Method 1: Total magnetic moment $$ \begin{align} \vec{\mu_J} &= ...
3
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3answers
188 views

Is $0 | \psi \rangle=0$?

For example, the spin operator for spin 1 particle is $\hat{S}_z\doteq\hbar\begin{pmatrix} 1&&\\&0&\\&&-1\end{pmatrix}$ for state ...
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1answer
53 views

Why can't de Broglie waves be electromagnetic in nature?

We know that the wavelength of de Broglie waves for a photon is same as that of the wavelength of the electromagnetic radiation that carries this photon. Doesn't this prove that matter waves are em ...
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2answers
118 views

The Delta-Function Potential

I'm reading through Griffiths Intro to QM 2nd Ed. and when it comes to bound/scattering states (2.5) they say: $E<0 \implies$ bound state $E>0 \implies$ scattering state Why doesn't this ...
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2answers
69 views

Should the eigenkets be weighted in $|P\rangle = \sum\limits_{r}|\xi^r\rangle$?

Page 37 of Dirac's book The Principles of Quantum Mechanics, states The condition for the eigenstates of $\xi$ to form a complete set must thus be formulated, that any ket $|P\rangle$ can be ...
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70 views

Difficulty evaluating a complex integral on Griffiths

This actually a question from Griffiths QM. (Q2.21) I have difficulty understanding integrals involving imaginary components. In this example, it looks like the first term (encircled in red) explodes ...
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1answer
71 views

Ground state of BCS mean field Hamiltonian

I have question following the logics of BCS Theory regarding the ground state. First let me recap the logics of textbooks, for example, by Carsten Timm . After obtaining the interacting BCS ...
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81 views

What is the difference between correlation and entanglement?

I have read that not all correlated states are entangled. What is the difference between the two? Mathematically, it was stated that a system which can be put in the form of ...
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55 views

Hamiltonian for Electron in Magnetic Field with Symmetric Gauge in Polar Coordinates

I am new on the board and have a question about how to write the Hamiltonian for an electron in a magnetic field rotating at a fixed radius. I would like to write the hamiltonian using the symmetric ...
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1answer
131 views

Can Bell's inequality violation be explained by the will of the scientist somehow affecting the experiment?

As far as I know, there are three possible ways to explain violation of Bell's inequality: violation of realism, violation of locality and violation of freedom. The first two are pretty ...
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358 views

What is meant by the spin of a particle? [duplicate]

I have been studying that electrons have quantum number called spin quantum number(s), this number can have either +1/2 or -1/2 value. If s=+1/2, the spin is clockwise and if s=-1/2, the spin is anti ...
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2answers
86 views

What does $g^{(2)}$ signify in quantum optics? And how to calculate it?

I have been studying research papers on Quantum Optics and non-linear optics. I frequently come across the $g^{(2)}$ value. What does it signify? What is its importance? How to calculate it? And ...
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1answer
45 views

Have $2s_{1/2}$ and $2p_{1/2}$ the same energy?

I have always known that p-states are more energetic than s-states. But in this picture I see the following: And it confused me. Could anyone explain if both levels have the same energy?