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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Fermi's theory of beta decay - Does Fermi's Hamiltonian have the wrong transformation properties?

I'm studying the theory of beta decays as proposed by Fermi in the 30's, and I found an inconsistency between the transformation properties that he claims for his Hamiltonian and the transformation ...
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1answer
110 views
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1answer
40 views

How to show the finite rotation of a spin-1/2 system?

I'm reviewing my quantum mechanics by going through Sakurai and Napolitano again and working out all of the derivations. I'm stumped (though I probably shouldn't be) on some algebra in the finite ...
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1answer
190 views

What is many-body bound state?

Bound state by definition is a state when particles are bounded together, so then "many-body bound state" would be bound state for a system of many bodies. Then I have several puzzles: 1. is the state ...
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0answers
24 views

1D Harmonic Oscillator: Eigenstate (|x=0>) at position x=0

Given an harmonic oscillator I need to calculate the eigenvector $|x=0\rangle$. Knowing that $$x|x=0\rangle = 0 \quad \Rightarrow \quad (a + a^\dagger) | x = 0 \rangle = 0 $$ I started to plug in the ...
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1answer
28 views

Generate exciton with parallel/anti-parallel spin

How can I experimentally generate excitons, controlling the spin-polarization of the participated electron and hole to be either exclusively parallel or anti-parallel?
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2answers
124 views

How does the Physics work for the Quantum Suicide thought experiment?

On page 5 of this paper written by Max Tegmark, Tegmark discusses a thought experiment called 'Quantum Suicide'. As far as I understand it, this experiment was created to show the experimental ...
3
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1answer
112 views

Quantized light-atom Hamiltonian

Suppose a "2-state atom" and a light field are quantized with the following Hamiltonians, respectively: $$\hat{H}_A=\hbar\omega_{21}\hat{\sigma}^{\dagger}\hat{\sigma}$$ and ...
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0answers
22 views

How does a Collider work? [closed]

How does a collider work, explained using various Physics theories (or if there is a main one) . How does the acceleration play a part in the individual sub-atomic kinetic levels. What happens when ...
5
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3answers
197 views

Can the absence of information provide which-way knowledge?

This seems an incredibly basic question, but one I've been unable to find an answer to on PSE; if this is a duplicate please point me in the right direction. Concerning a simple Young's double-slit ...
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3answers
290 views

Interference of overlapping wave functions

I'm a physical layman trying to understand some of the consequences of quantum mechanics. I understand that in the double-slit experiment, where we release individual photons in-phase, the ...
5
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3answers
228 views

How can I solve this quantum mechanical “paradox”?

Let a (free) particle move in $[0,a]$ with cyclic boundary condition $\psi(0)=\psi(a)$. The solution of the Schrödinger-equation can be put in the form of a plane wave. In this state the standard ...
3
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1answer
105 views

How I can prove the Commutation between hamiltonian and Runge-Lenz vector? [closed]

I am a undergraduate student in physics. I found this page that shows a way to prove the commutator between Runge-Lenz vector and Hamiltonian .$\left [\hat{A}_{i},\hat{H}\right]=0$ I believe he did a ...
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0answers
43 views

Landau levels in uniform magnetic field

Intro Landau levels are obtained by gauging the vector potential to be $$ \vec{A}=\left(-By,0,0\right) $$ By which the Hamiltonian: $$ H={1\over 2m}\left(\vec{p}-q\vec{A}\right)^2 $$ can be ...
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3answers
970 views

What is the physical interpretation of the density matrix in a double continuous basis $|\alpha\rangle$, $|\beta\rangle$?

(a) Any textbook gives the interpretation of the density matrix in a single continuous basis $|\alpha\rangle$: The diagonal elements $\rho(\alpha, \alpha) = \langle \alpha |\hat{\rho}| \alpha ...
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0answers
26 views

Could my idea of Faster-Than-Light communication using quantum entangled particles be feasible? [duplicate]

I am most likely completely off but I have an idea on how we might be able to exchange information using spins only (provided that we prepare for the exchange of information): We communicate using ...
3
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1answer
46 views

What is meant by taking the partial derivative of the Hamiltonian in this situation?

I'm doing a computation involving the quantum mechanical harmonic oscillator, and I have an expression of the form $\frac{\partial}{\partial \omega} \hat{H}$ where $$\hat{H} = \frac{1}{2m} \left( - ...
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0answers
44 views

Two black holes prepared from different initial states

I have asked a similar question, I would like to reformulate it in more details. Here is a thought experiment: Assuming we can create black holes by squeezing photons, we can then prepare two ...
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2answers
83 views

According to many worlds interpretation, to which world will I go?

From my understanding, many worlds interpretation views the actual world (universe) has many branch points. For example, coin flipping may cause two outcomes, but I will experience only on outcome or ...
5
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4answers
605 views

Why do electrons jump between orbitals? [duplicate]

When an electron is excited to higher energy levels, it will jump back to the same level from which it was excited. Why does it develop "sentiment" with that level?
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32 views

Implications for measurement of an initially localized free particle's wavefunction spreading out to infinity?

So, I have been attempting to wrap my head around what happens to a free particle that is initially localized to one spot. It seems that due to their different frequencies, the particle's wavefunction ...
0
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1answer
39 views

Thomas-Fermi approximation for cold atoms in a 1D harmonic potential

The Time-independent Gross-Pitaevskii equation is $$ \mu{\phi(x)}=\Big(\frac{-\hbar^{2}}{2m}\nabla^{2}+V_{ext}(x)+g|\phi(x)|^{2}\Big)\phi(x) $$ From Thomas-Fermi approximation, $$ ...
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5answers
16k views

How do electrons jump orbitals?

My question isn't how they receive the energy to jump, but why. When someone views an element's emission spectrum, we see a line spectrum which proves that they don't exist outside of their orbitals ...
0
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1answer
26 views

Implication of rotational symmetry on scattering matrix/ scattering cross-section [closed]

How does the rotational invariance helps simplifying Non-relativistic quantum scattering problems? Is there any any additional information that can be extracted about the scattering amplitude? It ...
0
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1answer
90 views

Is a larger black hole a faster or a slower processor?

For a remote observer, a black hole with mass $M$ has a temperature $T=1/M$. Now I am confused with the problem: A larger black hole can achieve a task faster or slower if it's regarded as a kind ...
14
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219 views

Has Jaynes's argument against Bell's theorem been debunked?

As a student of theoretical physics I'm well acquainted with the multitude of crackpot ideas attempting to circumvent Bell's theorem regarding local hidden variable theories in quantum physics. ...
2
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1answer
195 views

Question on spin-orbit interaction

When you study the spin-orbit interaction in quantum mechanics, even for a simple hydrogen atom, you find only the electric field in the nucleus reference system, while in the electron reference ...
2
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4answers
146 views

Is what statisticians call a “random variable” what physicists call an “observable” in QM? [duplicate]

I read at http://www.statlect.com/fundamentals-of-probability/random-variables that A random variable is a variable whose value depends on the outcome of a probabilistic experiment. Its value is ...
2
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2answers
93 views

Higher orders in perturbation theory

I would like to compute an energy level up to many orders in perturbation theory. My difficulty right now is not in the calculation itself but in understanding the algebraic structure of the higher ...
2
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4answers
153 views

Regarding the usage of 'classical potentials' in quantum mechanics

I am familiar with basic quantum mechanics and I know that there is no concept of 'force' in quantum mechanics, unlike in classical mechanics. Problems in quantum mechanics are solved by writing down ...
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0answers
36 views

Proof that a Hermitian Matrix is not defective?

I am taking an introductory course into Quantum Mechanics. To me to seems pretty simple to prove most properties of Hermitian operators. However, I am stuck at an edge case, proving that if an ...
8
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3answers
5k views

Bell's theorem for dummies, how does it work?

I've been reading up on theoretical physics for a few years now and I feel like I am starting to get an understanding of particle physics, at least as much as you can from Wikipedia pages. One thing ...
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0answers
35 views
8
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1answer
206 views

Why does the conjugated $\pi$ bond not violate the Pauli Exclusion Principle?

Let's look at the molecule 1,3 butadiene: $CH_2=CH-CH=CH_2$ and number the carbon atoms 1 to 4 from left to right. The bonds between 1 and 2 and between 3 and 4 are double bonds: each ...
3
votes
1answer
42 views

What is a “dynamically generated scale” physically?

A theory like QCD with massless quarks in four dimensions has no explicit mass parameters in its classical Lagrangian. At the quantum level however, instead a mass scale Λ is generated dynamically at ...
2
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2answers
173 views

Good resources for learning/reviewing complex time propagator formalism

I studied this at the beginning of my graduate degree but have to review it for my graduate exam. If it's not clear I'm talking about the $\beta = \frac{it}{\hbar} $ turning the integral of your ...
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1answer
669 views

Where can I find beginner's information about quantum mechanics? [duplicate]

Possible Duplicate: Popular books on QM I hope that this question is suitable for this site. I am interested in reading up on quantum theory so that I can reasonably understand the ...
2
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3answers
985 views

J.J. Sakurai book on Q.Mech [closed]

I just want to ask how recommended is the book on quantum mechanics by J.J. Sakurai. Is it any good as an introductory text? And are there better suggestions (substitutes)?
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1answer
43 views

Why does quantum mechanics produce different predictions for Bell test experiments than classical mechanics?

I understand that experimental results from Bell test experiments have shown that measured correlation is a cosine function of the angle between the detectors. What I am struggling to grasp is why ...
3
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0answers
62 views

What are fragmented condensates?

It is defined that if more than one eigenvalue of the one-body density matrix are macroscopically occupied the condensate is said to be fragmented. $$ n^{(1)},n^{(2)},...=\mathcal{O}(\mathcal{N}) $$ ...
2
votes
1answer
68 views

Conservation of momentum in infinite square well

This is inspired by Griffiths QM section 2.2, on the infinite square well, which is about how far I've gotten (so, sorry if this is addressed later in the book). For any given starting wavefunction, ...
5
votes
1answer
270 views

Wick's theorem for calculating OPE

I am trying to understand a calculation using Wick's theorem. Let $T(z)$ be the analytic part of a stress-energy tensor, and $\phi(z)$ a free boson field. Now, ...
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1answer
113 views

Existence of bound states in 3D Yukawa potential

For a 3D Yukawa potential $$ V(r) = - \lambda { e^{-Mr} \over r}. $$ Bargmann's upper bound can be read as necessary condition for the existence of at least one bound state; we want $N_l>1$ and ...
1
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1answer
51 views

Quantum bases conversion ($S_x$, $S_y$, $S_z$)

As part of several of my homework problems on the subject, I've had to convert between bases, for instance $|+\mathbf{x}\rangle$ in the $S_z$ basis $\left( \frac{1}{\sqrt{2}}\left( |+\mathbf{z}\rangle ...
0
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1answer
88 views

Galilean relativity in QM

Intro I've been trying to show that the generator of boosts can be written in operator form as can be seen here, as: $$ B = \sum_i m_i x_i(t) - t \sum_i p_i $$ As a reminder the transformation ...
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1answer
118 views

Relationship Between Stopping Voltage and Photocurrent

Online, I found a graph of photocurrent vs. stopping voltage: And I can’t figure out how photocurrent and stopping voltage have such a relationship. Stopping voltage is proportional to maximum KE ...
3
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1answer
82 views

Evaluating path integral

I am having some trouble remembering how to evaluate path integrals involving multiple particles. Suppose that I have two interacting particles with Lagrangian $$L= \frac{1}{2}m \dot y^2-\frac{1}{2}m ...
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0answers
40 views

Black hole evaporation, mass or bit?

Usually when we talk about black hole evaporation, mass or energy is taken as the target and the evaporation time is computed based on mass loss in a given time period. Is there any work to analysis ...
3
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1answer
75 views

What makes Bell's original inequality unsuitable for experiments?

Bell derives the inequality $$|E(\vec{a},\vec{b})-E(\vec{a},\vec{c})|\leq 1+E(\vec{b},\vec{c})$$ in his book Speakable and unspeakable in quantum mechanics. In this derivation he uses the assumption ...
12
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3answers
1k views

How to solve bound states of 2D finite rectangular square well?

I want to solve bound states (in fact only base state is needed) of time-independent Schrodinger equation with a 2D finite rectangular square well \begin{equation}V(x,y)=\cases{0,&$ |x|\le a ...