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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Books on Quantum Measurement

I have been trying to understand clearly the concept of non locality, hidden variables, quantum measurement etc through research papers. I also read Quantum Theory and measurment by Wheeler and Zurek ...
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4answers
46 views

Is energy of a quantum mechanical moving particle conserved?

From the Schroedinger equation $$ H\psi=E\psi, $$ if we want to measure the total energy of a quantum mechanical moving particle, then we have to apply the Hamiltonian operator to the wave function ...
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How does Sachs derive QM mass term from general relativity?

I am interested in finding Mendel Sachs' derivation of the mass term in the Dirac equation, using the covariant derivative terms. The discussions as to the merits of Dr. Sachs' work are often prefaced ...
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30 views

Time evolution of a discrete 1-d lattice of spin-(1/2) particles under a given Hamiltonian, or special cases thereof

I am trying to get some feel for the dynamics induced on a discrete 1-d lattice of spin-(1/2) quantum particles by the following Hamiltonian $\hat{H} = \sum_{i, j} r_{i j} \left[ ...
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37 views

Quantum mechanics for playmen [on hold]

I am a student who is working on a small game and I played around with the idea of using Quantum Mechanics as the base of the game. Which concepts and results would be cool to play around with ...
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21 views

Quantum Fields From Cluster-Decomposition Principle

My question is asking for an explanation of Weinberg's claim that QFT is the only way to satisfy Lorentz invariance and the cluster-decomposition principle. The theory is in his QFT Vol. 1. Below I've ...
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0answers
29 views

Functions of commuting operators and interactions

The action of a function of an operator $A$ can be determined by the action on the eigenstates of $A$. If I have two commuting operators $A$ and $B$ and $|a,b\rangle$ is a common eigenstate, I get ...
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1answer
738 views

Can conservation of momentum be violated?

The law of the conservation of momentum was accepted for year-hundreds. Even in Quantum field theory every particle collision must be momentum-conserving if there is homogenity in space. Can this ...
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33 views

Understanding the interpretation of wave-particle duality by W.L.Bragg

W.L.Bragg, the pioneer in x-ray diffraction, gave this lucid but vivid interpretation:"The dividing line between the wave & particle nature of matter & radiation is the moment now. As this ...
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54 views

How to connect these two formulations regarding the need for a density matrix in quantum mechanics?

I found these two formulations: The density matrix is: 1) "needed if we consider a system that is part of a larger closed system." 2) "needed for a system to be ...
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11 views

Commutation of Magnetic Translation Operator with Hamiltonian

How can I prove that magneic translation operator commutes with Hamiltonian where the translation operator does not for a non-zero non uniform magnetic field in general?
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2answers
79 views

Why do wave functions need to be normalized? Why aren't the normalized to begin with? [duplicate]

Before I started studying quantum mechanics, I thought I knew what normalization was. Just pulling off Google, here's a definition that matches what I've understood normalization to mean: ...
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62 views

Why tensor product? [duplicate]

Let $A$ an $B$ be two discrete observables (like spins). When exactly and why we have to consider their tensor product when talking about the mutual observation of the corresponding phenomena?
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46 views

How do we arrive on this kernel equation?

In Feynman and Hibbs, we see the following equation: $$K(b,a)~=~\sum_{\text{paths from $a$ to $b$}} \phi [x(t)] \tag{2-14}$$ which is valid always. Now, they write $$\phi[x(t)] ~=~ \text{const} ...
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1answer
35 views

Probability flux: spatial variation of the phase equal to momentum?

We can write any wave function as $$\psi(\vec x, t) = \sqrt{\rho(\vec x,t)}\exp{\left[\frac{iS(\vec x,t)}{\hbar}\right]}$$ for $S$ real and $\rho >0$. Here we interpret $\rho$ as the probability ...
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79 views

Funny quantum joke [duplicate]

Ok guys, this should be a fuzzy/silly question, but I have to understand why we do that (id est: the sign meaning). Let's suppose I want to describe, as a joke, the classical state of a coffee ...
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1answer
102 views

Does magnetic monopole violate $U(1)$ gauge symmetry?

Does a magnetic monopole violate $U(1)$ gauge symmetry? In what sense and why? Insofar as I know, there are at least two types of magnetic monopoles. One is the Dirac monopole while the other is the ...
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89 views

Quantum mechanics class [on hold]

I have a (strange) question about quantum mechanics graduate level courses. I am a first-year graduate student currently taking graduate quantum mechanics. We were given an exam this morning which I ...
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1answer
43 views

Fermions in a well

I have two identical fermions in an infinite potential well. They are non-interacting. How should I show that the first excited state is four-fold degenerate? Is the wavefunction just the ...
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2answers
130 views

How can mean value of a quantity $be$ an operator?

In Laundau & Lifshitz Quantum Mechanics. Non-relativistic theory in $\S29$ a problem is given: PROBLEM Average the tensor $n_in_k-\frac13\delta_{ik}$ (where $\mathbf{n}$ is a unit vector along ...
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2answers
77 views

Is the formula for Schrodinger's equation on Wikipedia incorrect?

http://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation#Time-dependent_equation On Wikipedia, the SWE contains a term called reduced mass. After consulting several peers, no one knows what this has to ...
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1answer
17 views
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39 views

Increasing Lattice Size in Quantum Espresso [on hold]

Quantum Espresso, a DFT simulation software, currently simulates only 8 atoms. How can be increase the number of atoms to say 64? Do we manually insert the ...
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1answer
79 views

What is the logic behind the thinking that electron must take a complicated path through the two slits?

Electrons moved in lumps, but unlike bullets, there was interference at the backstop. How? How can such an interference come about? Perhaps we should say: "Well, that means, presumably that it is ...
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39 views

Why are holes (in a semi conductor) regarded as particle?

Can I say that holes in a semiconductors are treated as current-carrying conventional direction ?
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46 views

What is the purpose of knowing the value of ground state energy of a potential well?

Using the formula $$E ~=~ \frac{\pi^2\hbar^2}{2 m a^2}$$ where $a$ is the length of an infinite potential well. It is apparent that as $a$ get smaller i.e. from a metal to the size of an atom, the ...
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39 views

Do electrons actually spin (what is spin)? [duplicate]

I read that electrons give off a magnetic field from their "spin" but I also read that they don't spin in the way we usually consider as spinning. So my question is what is spin, if particles aren't ...
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252 views

Meaning of spin operator

I am learning about spin in QM and I was wondering if $\langle{\psi}|\hat{S}_z|\psi\rangle$ where $\psi$ is a spin wave function, is a meaningful quantity? In the case of the Hamiltonian $\hat{H}$, ...
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1answer
52 views

An error in my understanding of entanglement

Based on my knowledge of quantum entanglement, I can set up a scenario which leads to a contradiction with the No-communication theorem. Please help me find the flaw. Suppose Alice wants to ...
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9 views

how far away from stable equilibrium is sys+res master equation valid?

just wondering how reliable the standard development of system+reservoir master equation model is from equilibrium. Thanks!
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33 views

Derivative of a function of an operator [on hold]

I would like to calculate something like $$K\left(z\right)=\dfrac{dF\left(A\left(z\right)+B\left(z\right)\right)}{dz}$$ i.e. the derivative of a function $F$ of a sum of two operators $A$ and $B$ ...
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61 views

What Quantum Entanglement is NOT? [on hold]

What are the most insightful experiments on Quantum Entanglement undertaken in the last few years showing what it is not? What insights did we gain from does constructive failures? Is there a current ...
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74 views

Size of hydrogenic atoms

Positronium consists of an electron and a positron. By what factor is a positronium atom bigger than a hydrogen atom? The solution has been explained to me. The characteristic length when solving ...
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1answer
91 views

Tensor product notation in quantum mechanics

I'm a bit confused about the use of Tensor products in Quantum mechanics. For instance if two electrons are in the state $\frac{1}{\sqrt{2}}(a(r_1)b(r_2)-b(r_1)a(r_2))\otimes \lvert \downarrow ...
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51 views

Quantum Physics..so what do you think? [duplicate]

We have de Broglie's equation for the wavelength of matter waves.well...we know that we neglect it in classical mechanics.Consider a space rocket or something that 's moving really fast.In a space ...
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31 views

How can a spinor represent an “epistemic” state?

I have read a lot of stuff on the seemingly endless debate on ontology/epistemology of the quantum state $\psi$. But I always wonder: how can a spinor be considered epistemic when $\psi$ really ...
2
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1answer
40 views

Connection between half and whole integer eigenvalues for orbital angular momentum [duplicate]

I have been trying to follow this derivation from Sakurai and Shankar, pulling from both. I would like to see how the following derivation can be extended to orbital angular momentum, and thus find ...
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2answers
65 views

The uncertainty principle and spin

I realize that this may be a very basic question, but I've been unable to find the answer elsewhere so thanks in advance for the help. Suppose an electron's spin is measured about an axis, and then ...
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10 views

Explanation for orientation entanglement

I have to write a summary for "orientation-entanglement": the state of an object/subsystem depends in general not only (locally) on its configuration in space, but also (nonlocally) on its topological ...
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1answer
61 views

What do atoms really look like?

When considering the orbital model of the atom it seems like the shape of each orbital corresponds the shape that contains a volume such that there is a 90% chance of an electron being there. I also ...
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Measuring the coherence between degenerate atomic ground states [on hold]

Given a 2-level atom with the degenerate ground state and excited state with $j_g =j_e =1/2$. Assume that initially the atom is prepared in pure state with all the population in its ground state. What ...
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28 views

Is there an equivalent probability distribution for fermions and bosons to the expression for distinguishable particles

So the particle distribution of two particles is simply $$ P_{12}=P_1(r_1)P_2(r_2) $$ where $ P_{12}$ is simply the modulus of the total wavefunction squared and $ P_1 $ and $ P_2$ are the the ...
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3answers
115 views

Expression of density operator

States in Quantum Mechanics can be thought of as density operators, i.e., positive semi-definite, normalized trace class operators on a Hilbert Space $\mathcal{H}$. In the case ...
2
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34 views

Are there resources for simulating and/or theoretically describing solitons?

Recently there are striking new ideas emerging on "lower level" dynamics with respect to quantum mechanics involving fluid mechanics principles, including hints of soliton-like aspects to particle ...
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35 views

Quanta Concept Time Line [on hold]

Just wondering why didn't soneone come up with quantum idea looking at the emission spectrum of matter vs. wait on blackbody ?
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32 views

Variational principle proof (summing over $n$)

From http://en.wikipedia.org/wiki/Variational_method_%28quantum_mechanics%29 $$= \sum_n \sum_m c_n^*c_mE_m \langle \psi_n|\psi_m \rangle$$ $$= \sum_n |c_n|^2E_n$$ I just want to better understand ...
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5answers
253 views

Why do we need a wave function?

Assuming our only aim is to solve double slit experiment (or other problems that can be mapped into that). Knowing that electron does some strange thing not expected of a particle, we need a function ...
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53 views

Are all properties entangled when one property is entangled?

When one or more particles are quantum entangled by say their spin property, do their other measurable properties (e.g., momentum, polarization, whatever?) become entangled as well?
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Wigner $d$-matrix for $j=1$

In Sakurai's Modern Quantum Mechanics p.198-199, he states that for the matrix $$J_y^{(j=1)} = \frac{J_+-J_-}{2i} = \frac{\hbar}{2} \begin{pmatrix} 0 & -\sqrt{2}i & 0 \\ \sqrt{2}i & 0 ...