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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How to derive De Haas–van Alphen effect?

I was reading Solid State Physics by Kittel and they manage to derive De Haas–van Alphen effect by invoking the Bohr-Sommerfeld model. This feels unsatisfactory to me. Can someone derive this using ...
3
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72 views

How to check whether Schrödinger's cat was in superposition of states?

Suppose we can make an arbitrarily precise preparation of a Schrödinger's cat (and isolate it arbitrarily well so that decoherence is not a problem). If we prepare lots of cats in this state, what ...
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2answers
52 views

Eigenstate vs collapsed wave function

An eigenstate, or determinate state, is a state where the measurement of some observable always yields the same result. This means that the standard deviation of the observable is zero. If a ...
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23 views

Is it possible to get the (Pauli) repulsive term in the Lennard-Jones potential from theoretical considerations?

Title says it: Is it possible to get the form of the (Pauli) repulsive term in the Lennard-Jones potential from theoretical considerations, or is it purely found experimentally through fits?
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25 views

Continuum Wave Function for the electron

I'm trying to understand certain processes like the photoelectric effect and Bremsstrahlung. In Bremsstrahlung I need to use the wave function of an electron coming from the continuum, and there is ...
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49 views

Quantum relativistic effects

I was performing a thought experiment: let us assume an object is traveling so close to the speed of light that the length of the object is small enough for quantum effects to become noticeable to a ...
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1answer
24 views

Probability density function of a particle for computation [on hold]

I'm writing a program, part of which relies on a particle being able to change location similar to a how a real particle would behave (pardon my physics). For example, on a grid of 100x100, a ...
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2answers
50 views

When generalizing from discrete (but infinite) eigenstates to continuous eigenstates, Why do we change the definition?

The propagator function for discrete eigenstates is $$u(t)=\sum_{n=1}^{\infty}|E_n\rangle\langle E_n|e^{-iE_nt/ \hbar } \tag{1}\ .$$ But when we have continuous eigenstates, (like for the case of ...
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1answer
48 views

Question about angular momentum operator

To show that the eigenvalue to $L^2$ is proportional to $\hbar^2$ is shown from $L_z=xP_y-yP_x$ $p_y=-i\hbar\frac{\partial}{\partial y}$ $p_x=-i\hbar\frac{\partial}{\partial x}$ ...
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175 views

Particles that are distinguishable and indistiguishable at the same time [migrated]

Thinking about a question and my answer to it and another question I asked earlier. I've come up with the following problem: Consider two otherwise very similar marbles, a red one and a blue one. Let ...
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1answer
42 views

What is the exhaustive set of experiments a quantum theory has to satisfy?

Any theory that is to explain the world correctly has to provide a mechanism by which the interesting results of quantum mechanics happen (e.g. diffraction patterns, momentum/position uncertainty, ...
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43 views

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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74 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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31 views

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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45 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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1answer
45 views

Quantum mechanics for playmen [closed]

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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83 views
+50

Quantum Fields From Cluster-Decomposition Principle

I would like help proving Weinberg's claim (I've quoted him below) that quantum fields are an unavoidable consequence of merging particle-based quantum mechanics with both Lorentz invariance and the ...
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0answers
31 views

Functions of commuting operators and interactions [on hold]

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
764 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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2answers
75 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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2answers
70 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 ...
2
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2answers
84 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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1answer
73 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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1answer
48 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
38 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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84 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
131 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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91 views

Quantum mechanics class [closed]

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
45 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 ...
4
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2answers
147 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
81 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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17 views
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1answer
81 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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48 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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49 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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40 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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4answers
259 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
54 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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0answers
35 views

Derivative of a function of an operator [closed]

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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62 views

What Quantum Entanglement is NOT? [closed]

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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1answer
96 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
93 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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0answers
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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33 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
41 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 ...
0
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2answers
69 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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14 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
63 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 ...