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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Is the Fermi golden rule really accurate for calculating the life time of an atomic level?

In my impression, Fermi golden rule is routinely used in calculating the life time of an excited atomic level. But it is based on the first order perturbation theory, so it is not expected to be ...
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1answer
24 views

Are coherent tunneling and incoherent hopping belong to quantum interference?

What the accurate definition of quantum interference in molecule or molecules? In some case, there is coherent tunneling in a molecule junction while sometime it is incoherent hopping, or even the ...
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72 views

Vector operators in quantum mechanics

Vector operators $\vec{V}$ in quantum mechanics are usually defined as those that commute in a particular way with the spatial Angular Momentum $\vec{L}$: $[L_i,V_j]=i\hbar\varepsilon_{ijk}V_k$. I am ...
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42 views

How to calculate the frequency of oscillation of superposition states [closed]

Been working on this question for a while and I'm not sure how to go about it. Could someone point me in the right direction, particularly for the frequency question. The question is as follows: A ...
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1answer
39 views

If a system is in a state $L^2 =2 \hbar^2$ and $L_x=0$ why can't $L_z$ be 0?

A particle is in a state where $L_x=0$ and $L^2 = 2\hbar^2$. This means $l=1$ and $m_x = 0$. I will call this state $Y^x_{lm} = Y^x_{10}$ I wanted to know what possible values $L_z$ could have in ...
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51 views

Am I using the variatonal method correctly conceptually?

Given A particle in a potential well: $V=-V_0 \exp(-x^2 / L^2)$ Goal Use the variational method to approximate the ground state energy My proposal The well (For $L=1$ and $V_0=10$) has the following ...
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1answer
63 views

Proof that trace is independent of representation [closed]

$$\begin{align} \sum_{a'} \langle a'|X|a'\rangle &=\sum_{a',b',b''} \langle a'|b'\rangle \langle b'|X|b''\rangle\langle b''|a'\rangle \\ &=\sum_{b',b''} \langle b''|b'\rangle \langle ...
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2answers
78 views

Schroedinger Picture more general than Heisenberg Picture?

When thinking about the two pictures, what I found to be strange was: I can write the postulate of time-evolution in the Schroedinger picture by: \begin{align} i \hbar \frac{d}{dt} \lvert \Psi(t) ...
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13 views

Coupling between angular momenta of particles conserve angular momentum of each particle?

Suppose there are two particles in angular momentum numbers $j_1$ and $j_2$ respectively. Suppose there is some interaction that couple together the particles' angular momenta. As there is no external ...
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76 views

Does momentum space have a speed limit?

In ordinary $xyz$ space, the maximum velocity of propagation for mass-energy and/or information is $c$. So, my question: Is there also a maximum velocity of propagation in momentum ${p_x}{p_y}{p_z}$ ...
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32 views

How do calculate <p|x>? [duplicate]

In my quantum mechanics lectures it says that the relation between the basis $|x\rangle$ and $|p\rangle$ is given by: $\langle p | x \rangle = \Large \frac{e^{-ip x/ \hbar}}{\sqrt{2\pi \hbar}} \, .$ ...
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23 views

Is it better to learn (and work with) Dirac formalism from beginning of studying Quantum Mechanics? [closed]

I want to find the best approach to Quantum Mechanics. Should i start with learning the Dirac formalism(and maybe studying from a book like Shankar's which uses it from the get go) or should i start ...
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1answer
55 views

What is the group transformation property of photons under rotation?

Both the photon and the W boson are spin-1 particles. Under rotation W boson must transform under the 3-dimensional representation of SU(2). However, the photon has two degrees of freedom (or helicity ...
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4answers
99 views

Why does a black body radiate in all the frequency spectrum?

I understand why a black body absorbs every frequency(it is the definition of a black body!) but i do not understand why it also radiates at all frequency spectrum.
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15 views

“Wobble” caused by electron pole in magnetic field

Watching Leonard Susskinds "Quantum Entanglement" Lecture Series and in Lecture 1 he explains that when measuring the angle of an electron poles in lets say one axis that no matter what the ...
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1answer
62 views

Hamiltonian operator in spherical coordinates

I'm studying the hydrogen atom from a quantum mechanics perspective, but I'm having troubles understanding a step. Consider the stationary Schroedinger equation: $$\hat H \psi = E\psi$$ Let $M$ be ...
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1answer
50 views

Understanding the basic concepts of quantum mechanics using a model [duplicate]

I'm not an expert and I don't know if already exists something like the following model, but I wrote a simple (mental) model to understand the basic concepts of quantum mechanics. I want to know if ...
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1answer
63 views

Why does general relativity need space to be continuous? [duplicate]

http://www.askamathematician.com/2009/12/q-howwhy-are-quantum-mechanics-and-relativity-incompatible/ So I was reading this article because I'm new to this stuff and don't quite understand the ways in ...
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2answers
42 views

Double slit with observer?

https://www.youtube.com/watch?v=Xmq_FJd1oUQ Apologize if this is a dumb question, I'm just a kid trying to make sense of something that I'm new to. It shows the wave interference when you send a ...
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0answers
59 views

Alternatives to the Feynman Lectures [duplicate]

I wanted to get a grounding in quantum mechanics, and was directed to the Feynman lectures. I was told to start from Vol I and work my way up to Vol III, where all the quantum mechanics stuff is. As a ...
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39 views

How do I expand the state $| x \rangle$ in terms of another orthogonal basis?

In my quantum mechanics textbook it says that the relation between the basis $|x\rangle$ and $|p\rangle$ is given by: $\langle p | x \rangle = \Large \frac{e^{-ip x/ \hbar}}{\sqrt{2\pi \hbar}} \, .$ ...
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1answer
70 views

why does quantumn theory not reconcile itself with general relativity [duplicate]

Why has there not been a resolution in the gravitational effect between the two? It seems that quantum theory and Einstein disagree.
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1answer
60 views

Question about heisenberg uncertainty principle and single-slit diffraction

My question relates to this video illustrating the Heisenberg uncertainty principle. The video shows light being shot through a slit forming a spot on a screen. As the slit narrows, the width of the ...
3
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1answer
122 views

Why are the elements of the periodic table stable? [duplicate]

I apologize in advance for the stupid question, but I was wondering about neutron decay and elements. Taking for example one of the most simple elements, Helium. Helium is made by 2 neutrons and 2 ...
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2answers
139 views

Rigorous Mathematical Proof of the Uncertainty Principle from First Principles

While looking at an intuitive explanation for the Heisenberg Uncertainty Principle (related question below), there was a mention of an axiomatic approach to establishing the uncertainty principle. ...
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3answers
198 views

Does quantum mechanics break causality? [duplicate]

If quantum mechanics is probabilistic, there is no reason for a particle to be in one place and not the other, but particles do make up their minds... but how?
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3answers
81 views

What changes in the electrons before and after a voltage drop?

It is easy to visualize gravitational potential energy as a function of the position of height, and a change in this potential is manifested in a change in height. Further, by the work-energy theorem ...
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1answer
105 views

Understanding the delayed choice quantum eraser from a quantum information stand point

A continuation of Understanding the quantum eraser from a quantum information stand point What quantum circuit would correspond to delayed choice? In particular, the decision of whether to not to ...
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1answer
26 views

Magnitude of the band gap

In Kittels book on solid state physics (Introduction to solid state physics, p. 167, 8th ed.), he defines the band gap energy $E_g$ as $E_g = \int_0^1 U(x) [|\psi (+)|^2 - |\psi (-)|^2]$ where ...
2
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2answers
93 views

Quantum mechanics and Lorentz symmetry

The operator $P$ in quantum mechanics is the generator for the translation transformation. We have: $$\exp(iPa)|x\rangle=|x+a\rangle$$ Similarly, I think the operator $X$ is the generator for the ...
3
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1answer
106 views

Understanding the quantum eraser from a quantum information stand point

Is there a way to understand the quantum eraser experiment in terms of quantum information? In particular, is there a quantum circuit that would function as a quantum eraser experiment? The issue I'm ...
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3answers
88 views

Energy equation in Quantum Mechanics

We know that total energy of the system is classically continuous, but in quantum mecanics (QM) it is quantised. My question is: How can we use the conservation of energy equation to derive ...
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1answer
50 views

Is there a correlation between Brownian motion and cosmic microwave background radiation?

Is there any correlation between Brownian motion, the phenomenon of osmosis - compared to cosmic microwave background, the Noise we see in analog television? Brownian motion or pedesis (from Greek: ...
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3answers
133 views

Physical Explanation of Quantum Mechanics Notation? [closed]

CLARIFICATION: I just don't understand what the notations below mean and how to use them. ============= I just started taking QM, and the new notation is quite confusing. While the math makes a ...
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1answer
69 views

Coherent state path integral - derivation

I divided the time interval $[t_0=:t_i,t_f:=t_N]$ into $N$ steps $[t_{k-1},t_{k}],\, k=1,\dots, N$ and applied the resolution of unity for coherent states \begin{equation} ...
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1answer
45 views

Lorentz covariant completeness relation

Let be $$ P^\mu |p> = p^\mu |p> $$ i.e. $|p>$ is the eigen-vector of the 4-momentum operator. Where does the following Lorentz-covariant completeness relation come from? $$ \int d^4p ...
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39 views

Band gap origin

Many introductory books on solid state physics use images that I find confusing. For instance, one picture I see alot when reading about the band gap, is similar to this one: I understand that the ...
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1answer
36 views

Good book on quantum photonics and applications

I am just looking for an easy to read introduction to quantum photonics and possible applications. Terms like "Fock state" and "Photon (anti)bunching" should be understood after reading. Perhaps also ...
1
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1answer
24 views

3D Bravais Lattices in terms of $\mathbb{Z}^3$

I am looking at the definitions of Bravais Lattice on Wikipedia and I find that I can describe many of them in terms of a mathematical lattice $\mathbb{Z}^3$. cubic $\mathbb{Z}^3$ body-centered ...
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0answers
34 views

If energy and mass are inter-convertible by Einstein's $ E=mc^2$ then when does energy turn to matter? [duplicate]

I encountered this question, as I was reading up on Gravity. The author of my textbook says that the stars orbit a common center which is their center of mass. I somehow think that this fact might ...
1
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4answers
103 views

Heisenberg's uncertainity principle

In the Heisenberg uncertainty principle, $$\Delta x \cdot \Delta p \geq \frac{h}{4\pi}$$ The values of $\Delta x$ and $\Delta p$ are the standard deviations which we get from the probability ...
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35 views

Which is the best place to learn about Measurement theory in Quantum Mechanics?

I have read Leslie Ballentine's book on quantum mechanics. I want to learn measurement theory. I am aware of the book Foundation and interpretations of Quantum Mechanics by Auletta. But I want ...
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1answer
70 views

What do term symbols with a half-integer “$L$” like $^3[3/2]_{1/2}$ mean?

Atomic term symbols are used to notate the angular momentum content of the electronic states of an atom, and are normally written down as $$^{2S+1}L_J$$ where the state has total spin $S$, spin ...
2
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0answers
55 views

Is my expansion of the state $| x \rangle$ correct? [duplicate]

In my quantum mechanics textbook it says that the relation between the basis $|x\rangle$ and $|p\rangle$ is given by: $\langle p | x \rangle = \Large \frac{e^{-ip x/ \hbar}}{\sqrt{2\pi \hbar}} \, .$ ...
0
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0answers
30 views

Off-diagonal matrix elements of the Hamiltonian = transition rate?

Definition: In the tight binding Model $t_{xy}$ denotes the quantum mechanical amplitude that an electron hops (tunnels) from the site y to x. My Problem: In many models we have $t_{xy}=H_{xy}$ and ...
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2answers
101 views

Meaning of “realism” in quantum mechanics

When physicists doing work in quantum measurement, decoherence, Bells' inequalities etc. use the term "realism" what exactly do they mean? I'm looking for answers targeted towards, say, someone whose ...
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2answers
35 views

Quantum mechanics of electron beam and measurement

I'm trying to understand the following phenomenon quantum mechanically: Problem statement If I'm shooting an electron beam (using a vacuum tube for example) and I have a measuring device at a ...
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40 views

Delayed Quantum Erasure and fortune telling

Imagine the delayed quantum erasure experiment set up such that a switch adds or removes a mirror instead of a 50/50 silvered mirror at BSa and BSb. This would cause a person to be able to choose ...
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1answer
102 views

Modelling excitation loss in a quantum network: non-Hermitian Hamiltonian vs. Lindblad formulation

This question is about modelling quantum transport of a single excitation across a network of $N$ sites, subject to incoherent processes where the excitation is lost from the network. The Hamiltonian ...
3
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1answer
73 views

Holding an electron

Heisenberg has said that the position and velocity of a small object cannot be known 100% accurate. Now, suppose I take a big metal box within which there is only one electron (somehow). I don't know ...