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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solving for the density operator in the quantum Brownian motion master equation

I want to solve for the density operator in the quantum Brownian motion master equation, \begin{align} \begin{aligned} ...
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1answer
12 views

Hartree Fock equations

I don't understand how the Hartree Fock equations define an iterative method! For this discussion, I am referring to the HF equations as described here: click me! Basically if you guess a bunch of ...
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11 views

Why does the 'many paths' of a photon theory work?

Posted this on reddit a day ago, and I'm still struggling to grasp the concept explained to me in physics class:/ Following the explanation from this link: ...
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1answer
20 views

Permutation operator and second quantization

I just read that a permutation operator $P_{i,j}$ acts on a product state $|a_1,...,a_n \rangle \in H^n$ by $$P_{i,j} |a_1,...,a_i,a_j,...a_n\rangle = |a_1,...,a_j,a_i,...a_n \rangle .$$ Now my ...
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19 views

Triangular barrier in infinite potential well

Suppose I am looking to solve the wavefunction for the following 1D potential: $$\psi(x) = \begin{cases}V_0\frac{a-|x|}{a}&\quad\text{for}\quad|x|<a ...
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29 views

How is tunneling probability?

Let's say we have an alpha particle tunneling through a barrier of width 2 fm and height 30 MeV, and the alpha particle has an energy 1 MeV below that of the barrier. The tunneling probability is ...
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1answer
25 views

Probability with expectational value [on hold]

How can I calculate: $$P(T)=T^2 b^2 |<n| \delta (x) |n>|^2~?$$ Where $P$ is the probability.
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1answer
28 views

Expectation value of operators in quantum mechanics

Can the expectation value of an operator be zero?
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28 views

Show that a function takes the following form using the definition for the function of an operator

If $f(z)$ is a function with a Taylor series expansion $$f(z)=\sum _{ n=0 }^{ \infty }{c_n z^n },$$ then we define $$f(M)=\sum _{ n=0 }^{ \infty }{c_n M^n }.$$ First consider ...
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95 views

Have they really photographed light behaving both as a particle and a wave?

I just came across this article where they are claiming that they have photographed light behaving both as a wave and a particle! The paper has been published in Nature and I read the abstract which ...
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61 views

Fundamentals of Quantum Mechanics [on hold]

I am currently midway through the undergraduate quantum mechanics series at my university, and I am beginning to feel somewhat troubled by the some of the implications of the subject. We accepted some ...
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1answer
19 views

Fine Structure Correction

The fine structure correction is composed of the relativistic correction and spin-orbit coupling. The lowest-order relativistic correction to the Hamiltonian is $$ H_r' = -\frac{p^4}{8m^3c^2}$$ ...
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35 views

Solving Schrodinger Equation with Anisotropic Effective Mass

How can I discretize a time-independent Schrodinger equation using the mass tensor and considering the valley degeneracy for the specific material at hand? I intend to investigate the confinement ...
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1answer
29 views

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
47 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
37 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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71 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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19 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
26 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
47 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
28 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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0answers
58 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
74 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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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 ...
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1answer
28 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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27 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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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 ...
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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
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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2answers
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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42 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
44 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 ...
2
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50 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 ...
2
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1answer
759 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
68 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
82 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?