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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Why does the nuclear volume scale (roughly) linearly with number of nucleons?

As far as I know, it is the fermi repulsion that gives a collection of protons or neutrons its finite size. But this only acts on indistinguishable fermions. If the protons and neutrons do not repel ...
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2answers
32 views

The delta function as an eigenfunction of the position operator explanation

$\delta (\textbf{r})$ can be interpreted as a wavefunction. [...] It is non-vanishing only for $\textbf{r}=0$. [...] $\delta(\textbf{r})$ is an eigenfunction of the position operator with ...
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1answer
29 views

Perturbation theory of states [on hold]

A particle in 1 dimension with mass $m$ is in potential well with $V = 0$ for $–a/2 < x < a/2$ and infinite potential elsewhere. The particle is initially in the state $n = 10^9 + 1$, with the ...
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0answers
44 views

What concepts could I teach to children in a game about quantum-mechanics?

I think that games can also be used to teach things to young people or childs, different than for example a book and could be more "direct" than teaching them all the math background, I would like to ...
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14 views

What is the best materiels for fixed target experiments with a linear particle accelerator? [on hold]

I need the best materiel for fixed target experiments using linear particle accelerators when accelerating electrons. By "best" I mean one that when the accelerated electron beam collides with it the ...
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1answer
25 views

Calculating values related to angular momentum and then their uncertainties [on hold]

Here is the problem: And here is my work (sorry it is handwritten, it would take a while to type this out) My problem is that I'm not sure if it's right or if it makes sense to keep getting 0 ...
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2answers
44 views

Normalization of wave function meaning…?

I just have one question. I'm doing a problem where I'm told to normalize a wave function, which is split up into two regions, namely where $r \leq r_0$ and $r > r_0$. My question is, why am I ...
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0answers
27 views

How to solve a difficult equation describing large vacuum fluctuations?

Suppose that a Quantum System can be described by the wavefunction $\psi(\vec{x},t)$, but due to the occurence of chaotic noise within the Quantum System, only the "filtered" wavefunction ...
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1answer
84 views

Can I state that $\Psi (x_1, \dots , x_n,t)= \sum_{i=1}^n a_i \psi (x_i,t) $ via superposition?

Given that the hamiltonian $\hat H$ of a system is a linear operator and $\dot \psi (x_i,t)$ does not depend on spatial coordinates $x_1, ..., x_n$ with bases $\hat e_1, ... , \hat e_n$ can I state ...
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51 views

Quantum mechanical expectation of angular momentum along different axes [on hold]

This is a question from Concepts of Quantum Mechanics by Mathur & Singh, and I don't know where I should start from: Show that, for a state $|j,m \rangle$, corresponding to a definite value of ...
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1answer
17 views

Uncertainty of energy for harmonic oscillator at ground state and first excited state

How does one calculate the energy uncertainty of the harmonic oscillator in the ground state and first excited state?
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1answer
73 views

How does one normalize this wavefunction? [on hold]

Here is the question: So I could write $ N = \dfrac{1}{{\sqrt{<Ψ|Ψ>}}} $, right? Considering the parentheses in the exponential term, it looks like a good idea to switch to spherical polar ...
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0answers
60 views

Can I have superposition equation? [on hold]

I would like superposition equation. I learn functions, boundaries of strings, boundaries of functions, differential equations, derivatives and integrals to understand superpositions from Mathematical ...
2
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1answer
26 views

Non-degenerate or degenerate perturbation theory for a non-degenerate level of a system with other levels degenerate?

To decide whether I have to use non-degenerate or degenerate perturbation theory, I have to look only on whether the energy level I am calculating corrections to is degenerate, the degree of ...
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0answers
24 views

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 ...
2
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0answers
57 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
44 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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0answers
22 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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23 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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0answers
45 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 ...
0
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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
47 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
41 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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40 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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4answers
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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41 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
43 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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0answers
27 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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31 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
757 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
71 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
66 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
votes
2answers
81 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
71 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
37 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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0answers
83 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 ...
4
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1answer
119 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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0answers
89 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
44 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
144 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
79 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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0answers
41 views

Increasing Lattice Size in Quantum Espresso [closed]

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
80 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 ...
2
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2answers
45 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 ?