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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6 views

Eigen energy of the Landau levels in a tilted magnetic field

The problem pertains to a fermi gas in a tilted magnetic field confined by a harmonic potential in the z direction. I chose the vector potential $(0,ax-bz,0)$. I obtain the following hamiltonain with ...
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0answers
23 views

Quantum mechanics: charged particel in magentic field [on hold]

Suppose a particle is moving in an uniform magnetic field $B$ in the $z$ direction. How do we find the time dependence of the position coordinate operators. I tried to work in the Heisenberg picture, ...
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0answers
24 views

Invariance of State Vector under Two Operations

I am trying to understand why if you measure one non degenerate operator you get a new state w1v let's say with w1 eigenvalue, then let's say u measure a new operator that has degenerate eigenvalue v ...
3
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1answer
47 views

Is there an angular velocity operator in quantum mechanics?

In classical mechanics we can write as velocity of a rotating object $\vec{v} = \vec{\omega} \times \vec{r} $ or in analogy the momentum $\vec{p} = m (\vec{\omega} \times \vec{r})$ using the angular ...
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2answers
33 views

How does the uncertainty product $\Delta x \Delta p$ behave for the bound states of the triangular potential?

As has been remarked earlier, if you take an unbounded potential $V(x)$ (so that all the eigenstates are bound) and you look at the uncertainty product $\Delta x\Delta p$ as a function of the index $n$...
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1answer
150 views

Why $\Delta x \Delta p_x$ for stationary states increase linearly with n?

Harmonic Oscillator $\displaystyle \Delta x\Delta p_x = \hbar (n+\frac{1}{2})$ Particle in a box $\displaystyle \Delta x\Delta p_x = \frac{\hbar}{2} \sqrt{(\frac{n^2\pi^2}{3}-2)}$ Similarly,...
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2answers
61 views

De Broglie- Bohm Quantum Theory

From what I have read the Standard Model of Particle Physics uses quantum mechanics,special relativity, along with other assorted mathematics to make predictions and provide a framework for QED, QCD, ...
11
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1answer
1k views

Eigenvalues and eigenfunctions of the exponential potential $ V(x)=\exp(|x|) $

For $a$ being positive what are the quantisation conditions for an exponential potential? $$ - \frac{d^{2}}{dx^{2}}y(x)+ ae^{|x|}y(x)=E_{n}y(x) $$ with boundary conditions $$ y(0)=0=y(\infty) $$ I ...
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1answer
29 views

Quantum vacuum thruster and conservation of momentum [duplicate]

I have been reading about the quantum vacuum thruster on Wikipedia and I think I understand the idea of virtual particles being created and destroyed but what I don't understand is how this is ...
8
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2answers
834 views

How should Dirac notation be understood?

If vectors $|\vec{r}⟩$ and $|\vec{p}⟩$ are defined as $$ \hat{\vec{r}} |\vec{r}⟩ = \vec{r} |\vec{r}⟩ \\ \hat{\vec{p}} |\vec{p}⟩ = \vec{p} |\vec{p}⟩ $$ then one can see that products like $$ ⟨\vec{...
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0answers
113 views

What does the Free Will Theorem Imply? [on hold]

Sorry if discussion of the Free Will Theorem belongs in the philosophy section, but as it is a physics theorem and what I am asking isn't philosophical, I thought I would post it here instead... ...
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1answer
20 views

Why must the separation constant be real in a time dependent wave function?

I'm not sure if I'm asking this right. I'm reading ''Introduction to Quantum Mechanics'' by Griffiths and in the chapter 2 exercises he asks to prove that the separation constant, $E$, must be real. ...
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1answer
21 views

Selection rules for electric quadrupole radiation

The selection rules for electric quadrupole radiation in a Hydrogen-like atom are: $$ \begin{aligned} \Delta l &= 0,\pm2 \hspace{1cm}(l=0\leftrightarrow l'=0 \textrm{ is forbidden}) \\ \Delta m &...
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0answers
70 views

Why don't we have to go through the Lagrangian in QM? [duplicate]

In classical mechanics, I remember whenever we calculated the Hamiltonian, we'd first have to calculate the Lagrangian, and then we'd get the Hamiltonian through the definition: $$H= \sum\dot q_ip_i-...
1
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1answer
26 views

Why can precomputed sets of lattice QFT field configurations be used to measure arbitrary observables?

My knowledge of quantum mechanics is rusty and my understanding of (lattice) quantum field theory on a very novice level at best, so it is likely my whole question is based on completely wrong ...
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0answers
16 views

How to apply the time evolution operator on a 2 level system

I'm struggling to understand how to actually solve analytically the time evolution of a given initial state with the Hamiltonian \begin{equation} H =\epsilon*\sigma_z + \Delta*\sigma_x, \end{equation} ...
3
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1answer
421 views

Fourier Transforms of position and momentum space in Quantum Mechanics

Fourier transformations: $$\phi(\vec{k}) = \left( \frac{1}{\sqrt{2 \pi}} \right)^3 \int_{r\text{ space}} \psi(\vec{r}) e^{-i \mathbf{k} \cdot \mathbf{r}} d^3r$$ for momentum space and $$\psi(\vec{r}...
0
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1answer
72 views

Applying angular momentum operator [on hold]

How are the algebraic steps to applied the angular momentum operator defined as: $$\hat{L}=-i\hbar[r\times\nabla]$$ to $$\Psi=a~ \psi_{431}$$ where the $\psi_{nlm}$ are the eigenfunctions of the time ...
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0answers
19 views

about the motion of electrons inside the atom [duplicate]

My question is very basic question.I am somehow not able to understand it. bohr's theory says that the electron can only revolve in orbits which they have quantised angular momentum so they must ...
5
votes
1answer
178 views

why the Laughlin's wave function is an incompressible quantum state?

some comments about the meaning of an incompressible quantum liquid are posted here: Incompressible quantum liquid In the same context, the Laughlin's wave function for a filling factor of 1/3 ...
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3answers
117 views

What is the Difference Between Quantum and Classical Interference

I was reading about Quantum decoherence and I came across this quote, "decoherence has irreversibly converted quantum behaviour (additive probability amplitudes) to classical behaviour (additive ...
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0answers
19 views

Function of operator quantum mechanics [duplicate]

Help me to prove this $$e^Ae^B=e^{A+B}e^{\frac{1}{2}[A,B]}$$ $A$ not commute with $B$, but $A and $B commute with $[A,B]$.
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1answer
100 views

What is the difference between active and passive transformations in Quantum Mechanics?

I am trying to understand what each transformation means and what their differences are but many books that don't state which transformation they are referring to make it a bit confusing to understand ...
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0answers
10 views

Specific microstate(s) corresponding to total angular momentum quantum number

Given a certain number of electrons in a certain electronic configuration (say, d$^2$ or (n$_1$p)(n$_2$d)), all combinations of the quantum numbers $m_l$ and $m_s$ can be constructed. Each of these ...
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0answers
32 views

Understanding the relationship between Phase Space Distributions (Wigner vs Glauber-Sudarshan P vs Husimi Q)

I am moving into a new field and after thorough literature research need help appreciating what is out there. In the continuos variable formulation of optical state space. (Quantum mechanical/Optical)...
3
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0answers
41 views

Quantum master equation vs regular master equation

I have a couple of related questions What is exactly the difference between the quantum master equation and the regular master equation? My understanding is that the normal master equation is used ...
0
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1answer
33 views

Group Velocity of guassian packet equals time derivative of mean position?

If I look at a gaussian wave package, and then interpret (in the usual Quantum-Mechanics Way) its square value as the propability density, then I can calculate a mean value for the position: $$ x_{...
2
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1answer
164 views

Para and ortho hydrogen angular momentum values

In Wikipedia, it is said that: Orthohydrogen, with symmetric nuclear spin functions, can only have rotational wavefunctions that are antisymmetric with respect to permutation of the two protons. ...
7
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2answers
519 views

How to promote algebraic expressions to operators in quantum mechanics?

Okay, I know that in quantum mechanics the quantum observable is obtained from the classical observable by the prescription $$ X \rightarrow x,\quad P \rightarrow -i\hbar\frac{\partial}{\partial x} $...
3
votes
1answer
99 views

How to evaluate possible values of spin of two photon system?

Photon hasn't well defined quantity such as spin. Instead of it, it is characterized by helicity $h$. Let's assume state of two photons in CM frame (with $\mathbf k$ being the momentum of one of ...
10
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1answer
339 views

In quantum mechanics, how exactly do we associate Hermitian operators to classical observables? [duplicate]

In a first course on quantum mechanics, everybody learns some version of the following statement: Postulate: To every classical observable $A$ of a physical system, there corresponds a Hermitian ...
4
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3answers
309 views

Spacetime and uncertainty principle

I only have limited knowledge of relativity and quantumphysics but as far as I know, the uncertainty principle relates the uncertainty of space and momentum of a particle. Einstein however, explained ...
3
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2answers
178 views

Problem with derivation of phonons in crystal

In this derivation of phonon solutions, everywhere, we are forcefully assuming the wavelike characteristics along the length of the chain. While all we can deduce for finding out the fundamental ...
0
votes
2answers
60 views

How do we determine the location of particles? [on hold]

Can someone explain how the location of a particle is determined both theoretically and experimentally (if possible)? Can the location of a particle be given by the uncertainty principle? (dividing ...
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0answers
30 views
3
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1answer
48 views

Can Light Waves Be Irregular?

From what I understand, electromagnetic radiation produced by an antenna is of the frequency that corresponds to the motion of the electrons moving around in the antenna. And I assume that the ...
6
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8answers
2k views

Prove that an electron in a hydrogen atom doesn't emit radiation [duplicate]

According to electrodynamics, accelerating charged particles emit electromagnetic radiation. I'm asking myself if the electron in an hydrogen atom emits such radiation. In How can one describe ...
0
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0answers
6 views

Calculating 2 particle Partial Trace for Density Matrix in Zeeman basis for a large number of Spins

I want to trace out all spins but 2 from a density matrix in the zeeman basis for N spins. For N=3 for example I would have the basisvectors: $ |S=1.5, m=-1.5\rangle =|000\rangle, |S=1.5, m=1.5\rangle ...
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0answers
29 views

Average magnetic dipole moment [on hold]

An electron in the hydrogen atom is described by the wavefunction: $$ \Psi = 0.5773\left(\psi_{431} + \psi_{432} + \psi_{321} \right) $$ where the $\psi_{nlm}$ are the eigenfunctions of the ...
0
votes
1answer
54 views

How to make an intuitive sense of the definition of Hermitian adjoint? [on hold]

How to make an intuitive sense of the definition of Hermitian adjoint? Why it is defined in that way? What is the different between operators and matrices?
12
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4answers
597 views

Curvature of Hilbert space

That may appear as a dumb question, but: Does Hilbert space have curvature, or is it a flat space? How and why?
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0answers
34 views

Relative velocity between phase velocity wave and a group velocity wave

It is said that material particles have a dual nature. A particle is associated with a wave which travels with phase velocity and the particle travels with group velocity. These are related by $$v_\...
1
vote
1answer
239 views

Thought Experiment: Force on magnets in a Stern Gerlach Experiment

Background: In the SG experiment, an inhomogenous magnetic field affects a force on particles passing between two magnets. "Measurement" takes place when a screen is placed on one end, blocking one ...
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1answer
28 views

Number of electrons in conduction band

As mentioned in a previous question, the number of electrons in conduction band in a semiconductor can be computed as follows: $$N = \int_{E_c}^{+\infty} g_c(E)f(E)dE$$ where $g_c(E)$ is the density ...
1
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2answers
32 views

Understanding Zeeman Splitting

I'm reading a standard modern physics history book ("Inward Bound" by A. Pais), and I realized I don't really understand Zeeman splitting well. In the section I'm reading, there's a short discussion ...
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0answers
29 views

Is my understanding of creation/annihilation operators' functional dependency correct?

I am trying to gain a little intuition about second quantisation, specifically about creation/annihilation operators. Lets say you quantise the free EM field (in 1d) and end up with the usual: $H=\...
54
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3answers
7k views

Is it possible to “see” atoms?

As per my knowledge, atoms are small beyond our imaginations. But there is an image on Wikipedia that shows silicon atoms observed at the surface of silicon carbide crystals. The image: How can we ...
-1
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1answer
492 views

Dirac Delta Potential and bound/scattered states

Why does the attractive Dirac Delta distribution (function) potential $V = \alpha\delta$(x) (for negative $\alpha$) yield both bound AND scattered states? Is this due to the definition of the Dirac ...
-3
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0answers
30 views

what is the rough motion of an electron in an atom [duplicate]

If The Uncertainity principle is true,then how does an electron move ?if the motion cannot be random also,then how does it occur?
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2answers
87 views

Can two different objects or system of molecules have different temperatures, but having same internal kinetic energy?

If I take an extreme case, where a body has only an internal potential energy with zero internal kinetic energy, does this body have a temperature? Another question related to it: if two objects A and ...