Tagged Questions

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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27 views

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 ...
2
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0answers
42 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 ...
7
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3answers
684 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' ...
2
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1answer
97 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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0answers
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 $f(x)$ ...
1
vote
1answer
28 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, ...
6
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2answers
84 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 ...
1
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1answer
56 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 ...
2
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1answer
80 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 ...
0
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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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2answers
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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0answers
51 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 = ...
6
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2answers
152 views

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 ...
4
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2answers
99 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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0answers
14 views

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 ...
2
votes
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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1answer
73 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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1answer
41 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 ...
0
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0answers
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 $f(x)$ ...
1
vote
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 ...
2
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3answers
191 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" ...
2
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2answers
42 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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2answers
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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0answers
28 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
109 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 ...
0
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0answers
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 ...
1
vote
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
votes
3answers
189 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 ...
0
votes
1answer
58 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 ...
2
votes
2answers
119 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
73 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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2answers
71 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 ...
2
votes
1answer
72 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 ...
3
votes
1answer
84 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 ...
1
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0answers
56 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 ...
0
votes
1answer
134 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 ...
3
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2answers
365 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 ...
2
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2answers
88 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 ...
1
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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?
2
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2answers
77 views

Domain of simple quantum harmonic oscillator

When discussing the spectral theory of unbounded operators, one often starts with an operator defined on a densely defined subspace of your Hilbert space, and then proves that the operator is ...
1
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0answers
59 views

Use a Delayed Choice Quantum Eraser to communicate Faster Than Light [duplicate]

In the experiment setup picture of the Delayed choice quantum eraser, photons reach D0 and shows a pattern, before its quantum entangled counterparts reach one of D1, D2, D3, or D4. The pattern ...
7
votes
1answer
71 views

What causes Paulis Exclusion Principle?

Currently I'm taking an astrophysics class and has now come across electron degeneracy. As far as I understand, the reason why white dwarfs and such, does not collapse, is due to this, meaning that ...
0
votes
0answers
41 views

The electron: why can't it have both momentum and position [duplicate]

Total amateur here. I've been watching video lectures on Quantum Mechanics and it's said that there is no way to know both position and momentum of an electron at the same time. But is it because when ...
4
votes
1answer
139 views

Why is Planck's constant the same for all particles?

This question came to me while reading "Where does de Broglie wavelength $\lambda=h/p$ for massive particles come from?". This question has a nice answer that explains that wave number has be ...
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0answers
19 views

Can anyone give me a simple proof for the sign change of electronic wavefunction when taken around a loop containing a conical intersection?

How and why does the sign of the electronic wavefunction changes when it is taken around a contour? For example, suppose the initial wavefunction is $f(s;S_0)$ at nuclear configuration $S_0$ and now ...
4
votes
2answers
77 views

Where does de Broglie wavelength $\lambda=h/p$ for massive particles come from?

I'm curious where the expression $p=\frac{h}{\lambda}$ comes from. I know that for light, the following is true: $E=pc$ and $E=hf$ so, $pc=hf \Rightarrow p=\frac{hf}{c}=\frac{h}{\lambda}$ But how ...
0
votes
1answer
43 views

How to understand the unitary? [closed]

In the page 219 of Mahan's Many Particle Physics(3ed), there exists a transform $$ S=c^{\dagger}c\sum_q\frac{M_q}{\omega_q}(a_q^{\dagger}-a_q)$$ In order to prove that the transformation relating to ...
4
votes
3answers
196 views

Why particle number operator $\hat{N}$ is $\hat{a}^\dagger\hat{a}$ rather than $\hat{a}\hat{a}^\dagger$?

Both $\hat{a}^\dagger\hat{a}$ and $\hat{a}\hat{a}^\dagger$ are Hermitian, how do we know which one represents the particle number?
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0answers
13 views

Split property for type III algebras entails practical separability

I am reading Halvorson's thesis (http://philsci-archive.pitt.edu/346/1/main-new.pdf), however I don't understand a proof at p.50 where he tries to explain why the split property allows a local agent ...
4
votes
1answer
68 views

Where is quantum physics with regards to the periodic table?

In his Lecture's on Physics (circa 1960's) Richard Feynman wrote that so far physics has only been able to model (solve) the hydrogen and helium atoms. So now, more than 50 year's later where are we ...