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 quantum-field-...

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107 views

Quantum physics and object location

If I understand correctly, according to quantum physics, subatomic particles can "leap" from one location to another (for example, from a location on earth to a location on the "other side" of the ...
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2answers
297 views

Separation of variables in various PDEs, physical meaning

The method of separation of variables produces an undetermined separation constant and a family of solutions indexed by the values of this constant. For instance, in the case of an infinitely long ...
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2answers
3k views

Nuclear Spin of Sodium 23

I am actually calculating the nuclear spin of Sodium 23. Here we have 11 protons and 12 neutrons. Now both the nuclei are short of the magic numbers. When I use the shell model for protons and ...
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2answers
284 views

Is the sign in the Schrodinger equation physical?

I always have trouble remembering the sign in factors like $\exp(\pm ik\cdot x)$ (I'll use mostly minus signature here) that arise in field theory. My mnemonic is to remember that the Schrodinger ...
4
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3answers
323 views

Some small questions about quantum spin and rotations

I'm studying about quantum-spin (in a syllabus about non-relativistic quantum-mechanics though), but I have some trouble understanding everything. So I would like to ask some small questions, which ...
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3answers
425 views

How to show that probability and statistics are very important in Quantum Mechanics?

I'm doing a research for my stats class in high school and I chose quantum mechanics as my subject. I narrowed down to electron localization in an atom and radial probability distribution. However, I ...
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1answer
218 views

Quantum mechanics problem? [closed]

I had a test on Quantum mechanics a few days ago, and there was a problem which I had no clue how to solve. Could you please explain me? The problem is: Let's look at the $\hat H=E_0[|1 \rangle \...
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2answers
529 views

If photons don't interact directly, how can electromagnetic waves interfere?

If photons don't interact directly, how can electromagnetic waves interfere? I know that photons can scatter via higher order mechanisms, but not directly. Does those mechanisms explain the classical ...
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0answers
153 views

Why is the following gauge transformation singular?

Suppose I have a single particle Hamiltonian: $H=\frac{p^2}{2m}+\frac{\hbar k_0}{m}\vec{\sigma}\cdot\vec{p}$, either for boson or fermion. I do a gauge transformation $e^{-ik_0\vec{\sigma}\cdot\vec{r}}...
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1answer
559 views

Quantum Field Theory and the Hartree-Fock approximation

I'm currently reviewing some of my notes on Quantum Field Theory (the version of Greiner) and I was wondering if QFT always works in the Hartree-Fock approximation ? Or at least that's what it seems ...
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2answers
448 views

Interpretation: probability form probability amplitude (free particle)

If you compute the probability amplitude of a free 1D non-relativistic particle with mass $m$, located at position $x_0$ at time $t_0$, for beeing detected at some other point $x_N$ at time $t_N$ you ...
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0answers
109 views

Approximate energy levels for the following potential

Let's have potential $$ U(r) = -U_{0}e^{-\frac{r}{a}}. $$ I need to find energy levels for particles moving in this field (for an arbitrary values of orbital number $l$). This task isn't exactly ...
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729 views

How are anyons possible? (another version)

I know that this question has been submitted several times (especially see How are anyons possible?), even as a byproduct of other questions, since I did not find any completely satisfactory answers, ...
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3answers
832 views

Heisenberg's uncertainty principle - $ \Delta p $

So I was reading this paper, "Limits to Binary Logic Switch Scaling—A Gedanken Model". The following is the paper's abstract: In this paper we consider device scaling and speed limitations on ...
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2answers
244 views

Is there a spin glass version of Prince Rupert's Drop?

Spin Glasses are known to converge to their ground state under Simulated Annealing. The word choice is especially interesting since annealing is also the name of a process performed on actual glass. ...
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1answer
116 views

Clarify formula in quantum perturbation theory

I'm studying perturbation theory in the context of quantum mechanics. My lecture notes say that in order to calculate the first-order correction of eigenfunction $\psi_n$, that is $\psi_n^{(1)}$, I ...
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1answer
98 views

Two particles state of a 1D massive scalar field

Perfectly localized states are not normalized so do not belong to the Fock space (they belong to the rigged version). Suppose we approximate localized states with gaussians, what is the mathematical ...
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3answers
439 views

How axiomatic is the symmetrization requirement (i.e. the Pauli principle)? (in QM)

I've so far always been told, that the symmetrization requirement is an axiom on the level of the Schrödinger equation and the statistical interpretation of the wave function (or it's absolute value). ...
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1answer
89 views

What is the commutator? [closed]

$e$ and $f$ are unit vectors, $L_e$ is defined by $L_e=eL$, where $L$ is of course the angular momentum operator. A similar definition for $L_f=fL$ The commutator that I can't solve: \begin{...
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1answer
141 views

Are composite bosons always bosonic (e.g. the pion-cloud surrounding the nuclei)?

The $\pi$-meson is a boson, but consists of quark-antiquark (fermions). It seems to me that at some energy level (equivalently distance) the inner structure (fermionic nature of the quarks) of the ...
2
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2answers
737 views

Wave function of a particle in a gravitational field

Suppose we have a particle with mass $m$ and energy $E$ in a gravitational field $V(z)=-mgz$. How can I find the wave function $\psi(z)$? It should have an integral form on $dp$. Any help would be ...
4
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2answers
226 views

why do we get continuous intensity in spectra?

we know energy levels of a molecule is discrete. So we should get only sharp peaks for any spectra. But in most of the spectra I see a continuous intensity? why is so? In the following spectra the ...
2
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1answer
89 views

The expansion of a function in powers of a parameter

In the perturbation theory for non-degenerate levels, the energy $E_n(\lambda)$ of an eigenstate $|\psi_n(\lambda)\rangle$ of the hamiltonian $\mathcal{H}=\mathcal{H}_0+\lambda \mathcal{H}_1$ (where $\...
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1answer
767 views

How to use the WKB approximation to find wave functions?

I'm trying to learn how to apply WKB. I asked a similar question already, but that question was related to finding the energies. Here, I would like to understand how to find the wave functions using ...
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1answer
118 views

Resonance Raman spectroscopy vs fluorescence

In Resonance Raman Spectroscopy we often want to avoid the fluorescence. But what is the problem with fluorescence . What we want is a shift between exciting line and emitted radiation and both can ...
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1answer
139 views

Quantum Mechanics mistake in partial trace

I have a given a density matrix by $\rho:=\frac{1}{2} |\psi_1 \rangle \langle \psi_1|+\frac{1}{8} |\psi_2 \rangle \langle \psi_2|+\frac{3}{8} |\psi_3 \rangle \langle \psi_3|.$ Where $|\psi_1\rangle :=...
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2answers
124 views

Basic Quantum Superposition

I'm looking to improve my understanding of quantum superposition. Consider the two-slit setup, where $|A\rangle$ is the state of the electron at the source, $|z\rangle$ is the state at some point on ...
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0answers
139 views

Bound states of the Schrödinger equation on $S^1\times \mathbb{R}^3$

I wana study the $\textbf{bound states}$ of a particle in the space $\mathbb{R}^3\times S^1$ which is under the effect of a time independent potential $V(\vec{r})$ but is free on $S^1$. So, I begin by ...
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2answers
348 views

Quantum barrier for photons [closed]

In quantum mechanics, a particle may tunnel through a barrier it would not be able to surmount in a classical sense. My question is this: What are all the factors that may prevent a photon from ...
2
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1answer
485 views

Time Dependent Position Operator

How does one find the time dependent position expectation value for a wave function? I thought we could simple take the time dependent wave and apply the position operator like normal, but this gave ...
4
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2answers
515 views

Why does $\ell=0$ correspond to spherically symmetric solutions for the spherical harmonics?

In quantum mechanics why do states with $\ell=0$ in the Hydrogen atom correspond to spherically symmetric spherical harmonics?
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1answer
1k views

How to apply the WKB approximation in this case?

I'm trying to learn how to apply the WKB approximation. Given the following problem: An electron, say, in the nuclear potential $$U(r)=\begin{cases} & -U_{0} \;\;\;\;\;\;\text{ if } r < ...
9
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2answers
669 views

Are all scattering states un-normalizable?

I am an undergraduate studying quantum physics with the book of Griffiths. in 1-D problems, it said a free particle has un-normalizable states but normalizable states can be obtained by sum up the ...
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2answers
87 views

Question about the shape of the waves [closed]

What is the molecular level reason behind the pattern (sine function) of the waves?
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2answers
186 views

When should one apply the unitary time evolution operator?

When is it appropriate to use $\hat U$, the unitary time evolution operator? For example, say I had a system in a certain potential that is changed to a different one at time $t = 0$. Would it be ...
13
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3answers
2k views

How does one determine ladder operators systematically?

In textbooks, the ladder operators are always defined," and shown to 'raise' the state of a system, but they are never actually derived. Does one find them simply by trial and error? Or is there a ...
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2answers
420 views

Detecting the presence of a delta potential

Suppose you have a particle in a box, and there may or may not be a Dirac delta potential somewhere in the box. How could one detect whether or not the potential is present? Furthermore: If there's ...
7
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1answer
358 views

How are the definitions of a coherent state equivalent?

I am trying to understand coherent states. As far as I could find there are three equivalent definitions and in general many sources start from a different one, still I fail to see their equivalence. ...
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4answers
837 views

Separability axiom really necessary?

I know other people asked the same question time before, but I read a few posts and I didn't find a satisfactory answer to the question, probably because it is a foundational problem of quantum ...
6
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1answer
216 views

How many of which particles are in Hawking radiation?

My understanding is that a black hole radiates ~like an ideal black body, and that both photons and massive particles are emitted by Hawking radiation. So for a low temperature black hole, photons are ...
2
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2answers
336 views

Higher moments of the kinetic energy operator in QM

I have set myself the task of studying the kinetic energy $T$ in a quantum mechanical system. For the latter, I use the simple case of the Hydrogen atom in the $n=1$ state. Then the wave function is (...
2
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1answer
378 views

what determines the direction of a single photon

Photon has momentum and energy.assume i am creating a nuclear fusion by fusing hydrogen nuclei into helium and a photon is created.Now which direction does it(single photon) moves or travel?can we ...
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0answers
32 views

Quantum Mechanisms for Isotope Fractionation

Are there any quantum properties that would enable isotope fractionation? For example, atoms with odd versus even numbers of neutrons are fermions and bosons, respectively. Has any work been done ...
2
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3answers
696 views

Normalization of basis vectors with a continuous index?

I have an infinite basis which associates with each point, $x$, on the $x$-axis, a basis vector $|x\rangle$ such that the matrix of $|x\rangle$ is full of zeroes and a one by the $x^{\mathrm{th}}$ ...
5
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2answers
273 views

Proof of conservation of information [duplicate]

After listening of some lectures of Leonard Susskind about black holes, he mentioned that conservation of information is one of the foundations of physics. After searching the web I cannot seem to ...
3
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6answers
268 views

Is position fundamentally different from other observables?

I apologize in advance for what might be a very naive question, and for its science-fictionesque flavor. It's still, I think, a real physics question. Suppose I have a (quantum) particle, whose ...
0
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1answer
246 views

Electron Decay, Why are there P and higher orbitals?

Related: Decay from excited state to ground state My confusion arose initially from the definition of binding energy being the lowest energy state (n=1) in the hydrogen atom. This, I assume, is ...
2
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0answers
72 views

Likelihood of the creation of a single unbound quark in the collision of very high energy particle beams

I am going over old exam and am not understanding the logic behind the answer given in the mark-scheme. A beam of protons and antiprotons attain energies of 1400 GeV in a synchrotron. Why is it ...
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1answer
113 views

What do they mean by $\langle u_i |O| u_j\rangle$ in quantum mechanics

UCSD's online QM notes, as usual, starts stating that QM operators are Hermitian and says that operator $O$ elements can be computed by $$O_{ij} = \langle u_j|O|u_i\rangle$$ The $u_i$ are ...
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1answer
119 views

What is quark transverse momentum?

When you google my question you get something on the order of 400 000 results but none of them explains how it is defined (No I didn't check them all). I know what the words quarks, transverse and ...