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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2answers
175 views

Precise meaning of composition of ket and bra, e.g. $|\psi\rangle\langle\psi|$

I'm currently studying density matrices, and have been frequently coming across the construction $$|\psi\rangle\langle\psi| \,.$$ What is the formal meaning of this composition? I understand ...
5
votes
1answer
146 views

Why don't we use Hamilton-Jacobi method in QM?

In classical mechanics, we usually try to find a set of coordinates by Hamilton-Jacobi method to transform the Hamiltonian to zero such that the coordinates are conservations. However, we never try ...
0
votes
3answers
236 views

Difference between expectation value and probability amplitude?

I was given a wave equation. I know that probability amplitude is the eigenvalue of an observable operating in a state. $$H| \psi\rangle = h| \psi\rangle$$ where $h$ is the probability amplitude of ...
6
votes
1answer
145 views

What are the restrictions on the Hamiltonian in QM?

In quantum mechanics, we usually write the Hamiltonian as: $$\hat{H}=\hat{T}+\hat{V}$$ But in classical mechanics, there are several reasons why it would not have this form: We've chosen some ...
0
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1answer
152 views

Difference between expectation values of $L^2$, $L_z$ and measuring $L^2$, $L_z$

I was given with this hydrogen radial wavefunction $$ R_{21} =\left(\sqrt{\frac{1}{3}}Y^0_1 + \sqrt{\frac{2}{3}}Y^1_1\right) $$ and was asked to find a) What are the expectation values of the ...
0
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1answer
292 views

Expectation value of energy from the position state of hydrogen atom [closed]

I was given with the position state of hydrogen atom: $$ R_{21} =\left(\sqrt{\frac{1}{3}}Y^0_1 + \sqrt{\frac{2}{3}}Y^1_1\right) $$ I am getting confused about getting the expectation value of ...
1
vote
2answers
654 views

Size of a photon

When detecting radio waves in space, we use very large telescopes or arrays of telescopes. But according to QM, aren't photons point particles when measured? Does a photon with a large wavelength ...
1
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0answers
67 views

How does $\bar{r}\times(\bar{\nabla}\times) - \bar{\nabla}\times(\bar{r}\times)$ relate to the orbital angular momentum operator?

When I attempted to calculate the following by hand $$\bar{r}\times(\bar{\nabla}\times\bar{F}) - \bar{\nabla}\times(\bar{r}\times\bar{F}),$$ I noticed some of the terms I extracted looked similar to ...
1
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0answers
147 views

Including special relativistic effects in momentum in Heisenberg's Uncertainty Principle

I've been told that an electron is somewhere within the space of $10^{-10}m$ and am supposed to find the uncertainty in its velocity. Simply applying $m\Delta x \Delta v \geq \frac{h}{4\pi}$ results ...
3
votes
1answer
263 views

Harmonic Oscillator potential, proof that Gaussians remain Gaussians?

I read in several papers that for a Harmonic Oscillator Hamiltonian in the time dependent Schrödinger equation a Gaussian wave packet remains Gaussian. Unfortunately I could not find any proof for ...
0
votes
3answers
226 views

On Group Theory: Symmetry Groups and Our Interest

Over the past few years, I've been doing a lot of self education in the Quantum Mechanics and General Relativity, and of course, there are mathematical elements of both doctrines that are matrices. ...
2
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2answers
1k views

Energy conservation limited by uncertainty principle

The way I learned it from practicing Fourier analysis and signal processing besides quantum mechanics, is that Energy conservation cannot be achieved in short time scales, and that limits energy ...
1
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5answers
140 views

EPR paradox: instantaneous vs very fast?

An EPR quantum experiment can be explained by instantaneous collapse of the wave function regardless of the distance separating a pair of entangled particles. But do we have the certainty that the ...
0
votes
1answer
194 views

Aufbau principle in modern quantum theory

What is the rigorous definition of the Aufbau principle and the mathematical model used for its description? From Wikipedia, we have that the principle postulates a hypothetical process in which an ...
17
votes
5answers
558 views

What does periodicity of $e^{-iHt/\hbar}$ mean in physical terms?

The unitary time evolution operator $U(t)=e^{-iHt/\hbar}$ has some distinct flavour of periodicity to it because of $e^{x+2\pi i}=e^x$. Is this periodicity reflected in any way in physical systems? ...
1
vote
1answer
220 views

Significance of magnetic translation operator defined in fractional QHE's description

What is the significance of the magnetic translation operator used in describing the Fractional Quantum hall effect? I was following Anthony Leggett's lecture video in which he defines these operators ...
4
votes
1answer
142 views

Why can we not apply perturbation theory in Born-Oppenheimer approximation

In Weinberg's Lectures on Quantum Mechanics, he mentions Unfortunately, we cannot simply use first-order perturbation theory, with $T_{nuc}$ taken as the perturbation and the state vectors ...
1
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1answer
83 views

Quantum Excitations

In the context of quantum mechanics, is the Schrödinger equation actually describing some sort of an actual wave in some field like light in EM field ? So all particles are actually waves in their ...
1
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1answer
109 views

What is $\langle \sigma_\mu \rangle$ $\langle \sigma_\mu \rangle$ for the Pauli Matrices?

What is \begin{align} \sum_{\mu=0}^{3} \langle \sigma_{\mu} \rangle^2 = ? \end{align} $\sigma_{\mu}$ are the Pauli matrices. The Bra-Ket notation is used in this question: \begin{align} \langle ...
0
votes
1answer
160 views

Many worlds interpretation

I think many worlds interpretation is inconsistent with the EPR paradox. Quantum mechanics says that particles are really in more places at the same time and the particle is really only probability ...
2
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5answers
398 views

Local EPR-experiments with photons in vacuum?

The principle of non-locality states "that an object is influenced directly only by its immediate surroundings." (Wikipedia) When two entangled particles are measured in an EPR experiment, we ...
5
votes
1answer
323 views

Are they the same thing: Wigner distribution in quantum Boltzmann equation and Wigner function in quantum optics?

We know that quantum Boltzmann equation (QBE) is an equation of motion for the interacting Green's function $G^<(\vec{x}_1,t_1;\vec{x}_2,t_2)\equiv\mathrm{i}\langle ...
2
votes
1answer
119 views

What are “parity considerations” in deciding the form of the Hamiltonian?

In "introductory Quantum Optics", by Gerry and Knight, the Jeynes model is considered. In this model of electron-EM field interaction the electron is approximated by a two state system ($\lvert ...
0
votes
0answers
51 views

motion of electrons [duplicate]

Do electrons move randomly, with no preference of directions? And why electrons don't fall into the nucleus? About this question, I read the article on Chemistry wiki, which says that when electron ...
8
votes
1answer
407 views

Double double-slit experiment

Suppose I have a double double slit experiment. That is, I have an electron gun in the center, that shoots entangled pairs of electrons in opposite directions, one to each double slit. I tried to ...
1
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1answer
660 views

Correspondence between wave function and state vector

I am confused with connection between state $| \psi \rangle$ of a quantum system and corresponding wave function $\psi(x)$ (at a given time). I have been told that for every state $| \psi \rangle$ we ...
3
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0answers
94 views

Does quantum mechanics require classical measurement apparatus?

I am trying to learn quantum mechanics and I have a question. Landau, in his quantum mechanics book says that it is in principle impossible to formulate basic concepts of quantum mechanics without ...
0
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1answer
75 views

Confusion about state of a quantum system

I am confused with the concept of state of a quantum system. First postulate of QM ussualy says that the wave function of the system contains all information about the state of the system. But reading ...
3
votes
0answers
427 views

Time Evolution Operator in Interaction Picture (Harmonic Oscillator with Time Dependent Perturbation)

1. The problem statement, all variables and given/known data Consider a time-dependent harmonic oscillator with Hamiltonian $$\hat{H}(t)=\hat{H}_0+\hat{V}(t)$$ $$\hat{H}_0=\hbar \omega \left( ...
0
votes
2answers
255 views

What is the reason behind why a quantum particle cannot be at rest?

So I've seen different reasonings for this; which is correct, or are they both corollaries of each other? 1) For a particle to be at rest, we would know its momentum and therefore by Heisenberg's ...
0
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0answers
27 views

Learning about group velocity, phase velocity and particle velocity [duplicate]

I am studying quantum physics and I would like to know a bit more in detail about group velocity, particle velocity and phase velocity. Can you guys suggest some books/online resources where I can ...
3
votes
2answers
169 views

Quantum Philosophy a la John Bell

I recently discovered this website http://www.quantumphil.org/ and wondering whether Quantum Philosophy is an actual field, or just an aspect of QM? Apologies if this is in the wrong place.
0
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2answers
52 views

Why does chemical potential smaller than zero mean nondegeneracy and vice versa

In Mudelung's book, Introduction to Solid-State Theory, I have a confusion about the statement. Here, $x$ should be $\frac{\mu}{k_B T}$. I am cofused about his statement. Why does $x<0$ mean ...
4
votes
2answers
197 views

Why does $c_{-k,-\sigma}$ create a particle with momentum $k$?

In Mudelung's book, Introduction to Solid-State Theory, I am confused by the following statement. For many applications a further simplification is helpful. The concept of the hole presents us ...
-2
votes
1answer
102 views

If the wave function can be collapsed, can we collapse the particle function? [closed]

No doubt it's been questioned before so what is the theory or experiment? If there is an experiment.
1
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0answers
57 views

How do I properly express adding perturbed states to unperturbed states?

I have a problem set due tomorrow, and the last problem is driving me nuts. Been combing through griffiths trying to find similar examples to no avail, so it'd be greatly appreciated if stackexchange ...
1
vote
1answer
209 views

Heisenberg's uncertainty principle - Planck's (reduced) constant divided by two or not? [duplicate]

The most common form of Heisenberg's uncertainty principle I've seen online is $$ \Delta x \Delta p ~\geq~ \dfrac{\hbar}{2}.$$ However, I also regularly see $$\Delta x \Delta p ~\geq~ \hbar. $$ ...
6
votes
5answers
750 views

Quantum Wave Mechanics

I am studying QM-I these days. Now, I just think of the wave function as just a mathematical function that defines the state of the particle at an instant and from it you can extract various ...
2
votes
3answers
179 views

Entanglement in single particle state

Is it possible that we have entanglement in different degrees of freedom of a singe particle. like spin and linear momentum .
1
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1answer
1k views

Calculating the energy of an electron given the wavelength

Okay, so I know that the wavelength of an electron is 5e-7m and I am asked to calculate its minimum velocity and hence minimum energy. Calculating the minimum ...
1
vote
1answer
137 views

Heisenberg picture usage - Merzbacher 14.106

I am trying to understand a line in the quantum mechanics book by Merzbacher, specifically the second line of equation 14.106. The problem is a forced quantum harmonic oscillator. The Hamiltonian ...
1
vote
2answers
144 views

A black torch to darken everything

Can we ever have a black colored (the color of the light and not the body's color) torch that darken (or dis-illuminates) everything? While compared to a normal torch it would function in an opposite ...
1
vote
1answer
80 views

Info request on studying QIT/QIS or QM with a Computer Science background [closed]

I've been considering a career change for a long time and recently discovered the Two-Slit Experiment, which, to put it frankly, blew my mind. I then started some hefty reading and investigation into ...
0
votes
2answers
71 views

energy of electrons outside an atom

The higher the quantum number(energy levels)m the higher the energy. What does the energy refers to? Kinetic energy, potential energy, or the total mechanic energy?
2
votes
1answer
86 views

Which types of particles are affected by the wave-particle duality?

If we take the double slit experiment as a way of demonstrating the wave-particle duality, which types of particles would show an interference pattern? For example, I know that electrons show such a ...
2
votes
0answers
182 views

Why do some terms vanish in first-order perturbation theory?

In first order perturbation theory, we usually express the first order perturbation in the eigenket of the perturbed Hamiltonian in the basis of the unperturbed Hamiltonian $H_{0}$: ...
-2
votes
1answer
64 views

Positron and other particles [closed]

Positron is a particle which has the same mass as an electron . But it has positive charge on it . When electron and positron combine, they annihilate each other with the release of energy in the ...
2
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0answers
50 views

Applications of Quantum Walks [closed]

Can someone explain to me what real world applications could potentially benefit from the study of quantum random walks? I have researched a fair amount on how quantum walks operate and their ...
2
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0answers
120 views

leaving 2-norm propelled probability implications

I am curious about why there are no further generalized probability structures used in Physics. The great revolution was moving away from one-norm system to a two-norm system. What happens if we ...
0
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0answers
107 views

Test for Many Worlds Hypothesis

If one actually ran an experiment similar to the Schrodinger's cat thought experiment, and ran it enough times (with the same cat) to get the confidence interval good enough, could one say that ...