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-...

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2
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2answers
478 views

Question regarding Schrödinger's equation

Here is my understanding of Schrödinger's equation and wave functions: (I'm considering the time independent equation.) The equation takes in values of energy as an input and, being a differential ...
2
votes
2answers
219 views

Wouldn't 3 or more particle entanglement allow passing classical information?

My (simple) understanding of entanglement is that by measuring the spin of one entangled particle, the other entangled particles' spin changes to the opposite of measured particle. This act of ...
4
votes
2answers
597 views

Is quantum uncertainty principle related to thermodynamics?

Would like to ask a question, but first i would like to say Hello Everybody in a way that plays the system, since some geniouses decided that one should not be able to say hello in a question. The ...
1
vote
1answer
221 views

Nuclear shell model - finite square well

I am trying to make a simplified approximation and solve Schrodinger equation in the finite square well to model the nucleus of Ca (shell nuclear model). The potential is $ V(r) = -V_0$ for $0<r<...
2
votes
2answers
50 views

Why the trap is needed in cold atom experiment?

In ultracold atomic gas experiments, the optical lattice provides a periodic optical potential to trap the atoms, why an extra trap, usually a harmonic trap is needed to trap the atoms?
1
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2answers
236 views

Stationary state of time-independent Schroedinger equation is always real valued function?

I am reflecting on the solution of the time-independent Schroedinger equation. My reasoning is that the stationary state of the time-independent Schroedinger equation must be a real valued function ...
2
votes
1answer
81 views

Angular momentum of anyons

Why is it true that anyons can have angular momentum taking any real value? Why aren't they restricted to the $j(j+1)$ integer values most are familar with?
3
votes
1answer
143 views

Electron momentum distribution and wavefunction in momentum space

Does there exist any relationship between the electron momentum distribution used in above threshold ionization and the wave function in momentum space? In other words, starting with the wavefunction ...
2
votes
1answer
2k views

How does temperature affect an electrical current

Synopsis I have read an interesting article J. Halderman et al. "Lest we remember: cold boot attacks on encryption keys" in computer science regarding cold booting. The paper discusses how the use ...
7
votes
2answers
498 views

Time-dependent Schrodinger equation from variational principle

In the paper, "Density-functional theory for time-dependent systems" Physical Review Letters 52 (12): 997 the authors mentioned that the action $$ A= \int_{t_0}^{t_1} \mathrm dt \langle \Phi(t) | i \...
2
votes
1answer
78 views

Alice sends random states in a channel, what Bob receives?

Suppose Alice prepares $\rho_x$ with probabilities $p_x$ and sends it to Bob. I would say this is the same thing as "Alice prepares $\rho = \sum_x p_x \rho_x$ and sends it to Bob", but Preskill's ...
3
votes
1answer
93 views

State with non-zero angular momentum - cannot be described by spherical harmonic?

For a state with non-zero angular momentum, why is it that it cannot be described by the spherically symmetric spherical harmonic?
1
vote
1answer
127 views

Euclidean functional Integrals

In the chapter "Uses of Instantons" from the book "aspects of symmetry" by Sidney Coleman I have come across the euclidean version of the path integral in semi-classical approximation. To evaluate the ...
1
vote
1answer
65 views

Atom state vectors kets

An atom with two energy levels has 2 states (excited and ground), represented by kets $|e\rangle$ and $|g\rangle$ respectively. The atom has energy $\frac{1}{2}E_\theta$ when excited and $-\frac{1}{2}...
6
votes
2answers
2k views

What does “causally connected” or “causes” really mean?

In a different thread, a user stated the following about events preceding or following other events: However, if the two events are causally connected ("event A causes event B"), the causal order ...
-3
votes
2answers
189 views

Quantum entanglement and special relativity PARADOX [closed]

Imagine two entangled atomic clocks. After we entangle them, we measure the time: it does has to be the same , right ? Now lets suppose that we entangle them , but don't measure them, then we plant ...
2
votes
0answers
47 views

How to load Bose-Einstein Condensates into an optical lattice?

In cold atom experiments, what techniques are used to load Bose-Einstein Condensates into an optical lattice??
6
votes
2answers
397 views

Naive questions on Goldstone modes and a possible duality relation?

For example, let's consider a 1D spin-1/2 ferromagnetic (FM) Heisenberg chain $H=-J\sum_{i=1}^{N}\mathbf{S}_i\cdot\mathbf{S}_{i+1}$ with periodic boundary conditions. Now we want to study its low ...
2
votes
0answers
102 views

Continuous Variable Entanglement Measure for the Statistically Mixed State

Can anybody tell me, which is the best entanglement measure for the Continuous Variable Entanglement of a Statistically Mixed State ? I have read that Schmidt decomposition is not valid in this ...
7
votes
1answer
286 views

ket vector with two “entries”

This is a very simple question. I am learning about angular momentum. In my lecture notes, the symbol $|\lambda,m_l \rangle$ was defined as a eigenfunction of a central potential. Two assumptions are ...
1
vote
2answers
241 views

details for the double slit experiment

In the double slit experiment with electrons, are all electrons going through the slits? If the electron gun is directed between two slits, than it should hit the central part between the slits, isn't ...
2
votes
3answers
293 views

Intuition/derivation behind the probability current definition

The definition is: $${\bf{j}} = \frac{\hbar}{2mi} (\psi^* \nabla \psi - \psi \nabla \psi^*)$$ However: Where ever I have looked, the above "pops out of nowhere". I was wondering how can I obtain ...
2
votes
0answers
65 views

superposition versus statistical mixture interpretation

I have an interpretation problem here. It is about the coherent state $$\left|\left.\alpha,\frac{\pi}{2\Omega}\right.\right\rangle = \frac{1}{\sqrt{2}}\left(e^{-\frac{i\pi}{4}}\mid\alpha\rangle+e^{\...
2
votes
1answer
154 views

Hamiltonian for the Periodic Kitaev Model

The Hamiltonian for a system of spinless fermions on a 1D chain (with chemical potential $\mu=0$) is given by $$ H=-\sum_j\left( c^\dagger_{j+1} c_j+h.c.\right)+\Delta \sum_j \left( c^\dagger_{j+1}c^\...
1
vote
0answers
19 views

Are states from an unpolarized source beam distinguishable or not

I have seen this pop up twice so far in my reading of Feynman Lectures III. For example, in the first equation of section 5-8 (it may take up to a minute for the equation to load), where the beam is ...
3
votes
1answer
166 views

How does a unique electron probability distribution correspond to one wavefunction?

I'm reading the Wikipedia article on DFT, and it says that there is a one-to-one correspondence between the ground state particle density $$n_0(\vec{r}) = N \int \text{d}^3 r_2 \int \text{d}^3 r_3 \...
5
votes
2answers
327 views

A modified version of the famous double-slit experiment

As far as I know, all the double slit experiments that were performed uses a light source (or electron source...) that emits photons at a "perpendicular" angle as this image shows: (will call it ...
8
votes
4answers
995 views

How can things be chaotic on a quantum level, yet tangible on a classical level?

This may seem basic, but I am wondering if anyone has any input on this topic. It doesn't make any sense to me (I mean I don't need to use the Schrödinger equation to find my cell phone...). I just do ...
2
votes
1answer
478 views

Unstable states and imaginary (complex) energy?

I came across the notion of complex energy while studying instanton method to study the unstable state. Unstable states are those which have energy with an imaginary part. But as we know Hamiltonian ...
0
votes
1answer
104 views

Hamiltonian Operator for Harmonic Oscillator

I have been solving the harmonic oscillator problem in quantum mechanics using Algebraic Method and since then I am consulting the books of Tannoudji and Griffiths for that matter. While studying both ...
0
votes
1answer
85 views

Time-dependent perturbation - details in derivation

I get confused about two things when deriving the time-dependent perturbative approach. We have the Hamiltonian $$H = H_0 + \lambda H^{(1)}$$ and we have solved (from Schroedinger) $$\dot{C_f(t)} ...
2
votes
4answers
16k views

What is wrong with the Bohr model?

What is wrong about the Bohr model? Many books say it is wrong but doesn't say why and I don't know why.
6
votes
3answers
743 views

Is there an inconsistency between Quantum and Classic in probability density of harmonic oscillator ground state?

Consider probability densities for a particle in the lowest energy state of a simple harmonic oscillator. The quantum mechanical probability density peaks near the equilibrium point and extends beyond ...
1
vote
0answers
66 views

EPR Experiments and Monogamy

Normally in an EPR experiment two measurements are performed on entangled particle pair. Only the particle pair is treated quantum mechanically and it is usually prepared in a state like $$ (\,\left|\...
1
vote
1answer
489 views

How to determine the transmission coefficient of a gaussian wave packet scattering on an finite square well?

I am doing a scattering simulation of a Gaussian wave packet on a finite square well. I have solved numerically the Schroedinger equation and I know the values of the wave function after the ...
-1
votes
1answer
56 views

Accleration and frequency

Recently, I was taught by my teacher that the acceleration of an electron in a Bohr Atom is equal to its frequency. I am confused and did not understand why it turns out to be equal.
1
vote
2answers
2k views

Interesting relationship between diffraction and Heisenberg's Uncertainty Principle?

I recently came across an interesting explanation of diffraction through an aperture which does not use Huygens' Construction but instead relies on Heisenberg's Uncertainty Principle: The ...
2
votes
1answer
263 views

Reflection Probability for Different Potentials - Quantum Mechanics

My question is above. Firstly, I don't actually know whether it is true or not (!). Secondly, if I were to try to prove it, then I have very little idea how to. The potential steps that I have always ...
9
votes
3answers
6k 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 ...
1
vote
1answer
142 views

Question about De Broglie Wavelength

I read that: The smallest wave packet we can build has a size on the order of the de Broglie wavelength $\lambda$ of a free particle moving with the same speed $v$. I haven't been able to find a ...
49
votes
9answers
3k views

Is the uncertainty principle a property of elementary particles or a result of our measurement tools?

In many physics divulgation books I've read, this seems to be a commonly accepted point of view (I'm making this quote up, as I don't remember the exact words, but this should give you an idea): ...
1
vote
0answers
70 views

Scattering of two particles - phase factor

I did see some posts on stackexchange on this matter, but I find them to be beyond my scope or not directly related to what I am looking for. I am reading Feynman Lectures III, chapter 4. It talks ...
4
votes
1answer
194 views

What are phase conventions in angular momentum and rotation calculations?

I work with complicated angular momentum calculations related to atomic physics; nevertheless, I never need to use anything related to a phase convention (apparently because it's taken care of in a ...
0
votes
1answer
75 views

Ladder operator on momentum basis

Since in Quantum mechanics momentum operator can be written in terms of ladder operators $$\widehat{p}=-i\sqrt\frac{{\hbar m \omega}}{2}(\widehat{a}-\widehat{a}^\dagger)$$ these operators operate on ...
0
votes
1answer
67 views

Crystal diffraction for waves vs particles

I thought that I understand the "Bragg's Law" understanding of crystal diffraction, but recently I read something that made me confused. I understand that if the planes in the crystal have ...
2
votes
1answer
204 views

Probability of being in the same initial state

If the Hamiltonian has basis of eigenvectors $\phi _1, \phi_2,..$ with corresponding eigenvalues $E_1,E_2,...$. I then define an observable $A$ by: $$A\phi_1 = \cos(\beta)\phi_1 + \sin(\beta)\phi_2$$...
1
vote
0answers
59 views

Quantum oscillator, position mean value problem

A quantum harmonic oscillator of mass $m$ and frequency $\omega$ is at time $t=0$ in the state: $$ \left|\psi(t)\right> = \sum_{n=N-\Delta N}^{N+\Delta N}\left|n\right>\frac{1}{\sqrt{2\Delta N +...
3
votes
2answers
138 views

How can a single quantum system be prepared in a particular mixed state?

Let's consider an electron in some sort of potential well. Suppose $|i\rangle$ is an $i$th eigenstate, and we want to prepare the electron in state with state vector (up to normalization) $|\psi_1\...
4
votes
2answers
348 views

Is Ehrenfest theorem equivalent to Bohr's Correspondence Principle?

Ehrenfest theorem is usually dubbed as the quantum mechanical equivalent of Newton's law and Griffiths states, in the first chapter of his textbook, that Ehrenfests theorem enables us to work with ...
3
votes
2answers
161 views

Two explanations of non-zero atomic radius

I have came across two separate explanations for why atoms have a positive atomic radius (as opposed to electrons "collapsing" into the nucleus). The first is via Heisenberg Uncertainty Principle, ...