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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Expectation value of the Hamiltonian [closed]

How to calculate expectation value of the Hamiltonian for hydrogen atom? $$\langle H \rangle_{\alpha l} \equiv \frac{\langle \psi_{\alpha l m}|H(r)| \psi_{\alpha l m}\rangle} {\langle \psi_{\alpha l ...
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Two-Photon Transitions

I'm reading these course notes on two-photon transitions at http://cua.mit.edu/8.421_S06/Chapter9.pdf But I can't understand why it looks like they do not allow for Autler-Townes splitting. In ...
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64 views

Reduced density matrix

During a course on quantum mechanics we've been talking about density matrices. Now I came across the following exercise. Consider a two spin $\frac{1}{2}$ systems, labeled 1 and 2. Calculate: ...
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34 views

Obtaining an angular distribution from the Klein-Nishina formula

I'm having trouble on how one might obtain an angular distribution from the Klein-Nishina formula for compton scattering of polarised photons, more specifically on how this report is obtaining it. ...
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Simultaneous measurement of non-commuting observables without uncertainty

A pair of non-commuting Observables $\hat{X}$ and $\hat{P}$ does not have a common set of eigenfunctions, i.e., it can not be measured simultaneously. Let us for the sake of simplicity assume that ...
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157 views

Does relativity violate uncertainty principle?

Let us say I sit on an electron. According to me the electron is at rest. Also, I will know the position of the electron accurately as I can take the electron as the origin. So, I know both position ...
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25 views

What does an eigenfunction which orthogonal to the general wavefunction mean , does it mean that the probablity of that eigenfunction is zero?

Imagine a wavefunction: $$ \Psi = C_1 \psi_1 + C_2\psi_2 + C_3\psi_3 + C_4\psi_4 $$ where $C_1$, $C_2$, etc are all constants and $\psi_1$, $\psi_2$, etc are eigenfunctions. If it is given that ...
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43 views

How it is possible that phase velocity of de Broglie wave may exceed velocity of light? [duplicate]

Phase velocity of de broglie wave may exceed the speed of light .Does this violate the relativity theory as we know nothing can overcome speed of light ??
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47 views

inverse problem for specific heat of fermion .. has been solved?

hi given the specific heat is given by an integral equation $$ C(T)=\int_{0}^{\infty}d\nu g(\nu)\frac{u^{2}}{(e^{u\nu}+1)^{2}}\nu^{2}$$ where $ u= \frac{h}{kT}$ my question is is the following ...
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1answer
54 views

Many-worlds interpretation (MWI) and conservation of energy [duplicate]

I am not an expert of many-worlds interpretation (MWI), and what I say may be stated incorrectly. In that case i welcome corrections. If the MWI is true and it explains quantum theory and it splits ...
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26 views

Is the transition electric quadrupole or magnetic dipole?

If a nucleus makes a transition from 0$^+$ ground state to 2$^+$ excited state, then will the transtion have E2 character, or M1? Or partly, both? Should the matrix elements of both E2 and M1 be ...
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17 views

Where can I find information on gas discharge tube mixes beyond the noble gases?

I have seen plenty of information on the noble gases, and oxygen and nitrogen. I haven't found much on other gases, or mixtures of gases. I don't really know where to look beyond google. I am in ...
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12 views

Multimode thermal state

A multimode thermal state is defined as: $ \rho=\sum_{\{n_k\}}|\{n_k\}><\{n_k\}|\prod_k\frac{<n_k>^{(n_k)}}{(1+<n_k>)^{n_k+1}} $ Is it also possible to swap the product and the ...
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75 views

Quantum computing with biological matter? [closed]

As a biologist with physics background I wonder whether there is a way to use biological matter to create quantum computers or at least to advance the field somewhat. Usually, my first feeling would ...
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7 views

type of photoluminescence depending on the FWHM

Depending on the FWHM of CdSe quantum dots, is it possible to estimate the type of dominant photoluminescence in question, as in excitonic luminescence is supposed to have a narrower spread than ...
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1answer
61 views

What's the microscopic and macroscopic effect of wavefunction dispersion?

In Quantum Mechanics (Merzbacher 2nd ed.), problem 2.1 asks us to derive the time evolution of a one-dimensional Gaussian wavefunction (formula given for $t=0$), assuming the velocity is in the $+x$ ...
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43 views

What type of physicist studies quantum physics the most? [closed]

I want to become a physicist, and I am particularly interested in quantum physics. I know quantum physics has applications in many branches of physics. Condensed matter physicists use it among others. ...
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1answer
34 views

Re-entering superposition

I've realized that I'm somewhat familiar with what happens when an system in a superposition is "measured". But not at all with what happens after. Example: If there is an electron in a ...
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48 views

Operator notation?

I'm starting out with many-body quantum theory, second quantization etc. by reading the book by Bruus and Flensberg. In the first chapter they write; "A given local one-particle operator $T_j$ ... ...
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4answers
65 views

What is meant by an excited atom?

I want to know how an atom is when it is excited. If an atom, due to collision of another fast moving atom, becomes fast moving as well, is that also an "excited state"?
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1answer
31 views

Z coordinate expectation value of the Hydrogen atom

I want to find $z-coordinate$ expectation value $\textbf{<z>}$ of the Hydrogen atom wave function $\psi_{1,0,0} = (\pi a^3_0)^{-1/2}e^{-r/a_0}$ in its ground state. I read in some text that ...
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27 views

Selection rules in a finite quantum well

I have a finite quantum well made of two different semiconductors with different bandgaps and I want to calculate the different transitions between the energy levels possible that I calculated in that ...
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1answer
86 views

Clarification about two forms of the wave function

The wave function in the position representation is $\langle\ x\rvert\psi\rangle$ = $ \psi (x) $ , where $ \psi (x) $ are the continuous coefficients that multiply the orthonormal basis vectors, i.e, ...
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45 views

Is the Fermi golden rule really accurate for calculating the life time of an atomic level?

In my impression, Fermi golden rule is routinely used in calculating the life time of an excited atomic level. But it is based on the first order perturbation theory, so it is not expected to be ...
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23 views

Are coherent tunneling and incoherent hopping belong to quantum interference?

What the accurate definition of quantum interference in molecule or molecules? In some case, there is coherent tunneling in a molecule junction while sometime it is incoherent hopping, or even the ...
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Vector operators in quantum mechanics

Vector operators $\vec{V}$ in quantum mechanics are usually defined as those that commute in a particular way with the spatial Angular Momentum $\vec{L}$: $[L_i,V_j]=i\hbar\varepsilon_{ijk}V_k$. I am ...
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42 views

How to calculate the frequency of oscillation of superposition states [closed]

Been working on this question for a while and I'm not sure how to go about it. Could someone point me in the right direction, particularly for the frequency question. The question is as follows: A ...
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1answer
39 views

If a system is in a state $L^2 =2 \hbar^2$ and $L_x=0$ why can't $L_z$ be 0?

A particle is in a state where $L_x=0$ and $L^2 = 2\hbar^2$. This means $l=1$ and $m_x = 0$. I will call this state $Y^x_{lm} = Y^x_{10}$ I wanted to know what possible values $L_z$ could have in ...
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51 views

Am I using the variatonal method correctly conceptually?

Given A particle in a potential well: $V=-V_0 \exp(-x^2 / L^2)$ Goal Use the variational method to approximate the ground state energy My proposal The well (For $L=1$ and $V_0=10$) has the following ...
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1answer
63 views

Proof that trace is independent of representation [closed]

$$\begin{align} \sum_{a'} \langle a'|X|a'\rangle &=\sum_{a',b',b''} \langle a'|b'\rangle \langle b'|X|b''\rangle\langle b''|a'\rangle \\ &=\sum_{b',b''} \langle b''|b'\rangle \langle ...
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78 views

Schroedinger Picture more general than Heisenberg Picture?

When thinking about the two pictures, what I found to be strange was: I can write the postulate of time-evolution in the Schroedinger picture by: \begin{align} i \hbar \frac{d}{dt} \lvert \Psi(t) ...
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Coupling between angular momenta of particles conserve angular momentum of each particle?

Suppose there are two particles in angular momentum numbers $j_1$ and $j_2$ respectively. Suppose there is some interaction that couple together the particles' angular momenta. As there is no external ...
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76 views

Does momentum space have a speed limit?

In ordinary $xyz$ space, the maximum velocity of propagation for mass-energy and/or information is $c$. So, my question: Is there also a maximum velocity of propagation in momentum ${p_x}{p_y}{p_z}$ ...
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32 views

How do calculate <p|x>? [duplicate]

In my quantum mechanics lectures it says that the relation between the basis $|x\rangle$ and $|p\rangle$ is given by: $\langle p | x \rangle = \Large \frac{e^{-ip x/ \hbar}}{\sqrt{2\pi \hbar}} \, .$ ...
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Is it better to learn (and work with) Dirac formalism from beginning of studying Quantum Mechanics? [closed]

I want to find the best approach to Quantum Mechanics. Should i start with learning the Dirac formalism(and maybe studying from a book like Shankar's which uses it from the get go) or should i start ...
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1answer
54 views

What is the group transformation property of photons under rotation?

Both the photon and the W boson are spin-1 particles. Under rotation W boson must transform under the 3-dimensional representation of SU(2). However, the photon has two degrees of freedom (or helicity ...
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4answers
99 views

Why does a black body radiate in all the frequency spectrum?

I understand why a black body absorbs every frequency(it is the definition of a black body!) but i do not understand why it also radiates at all frequency spectrum.
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“Wobble” caused by electron pole in magnetic field

Watching Leonard Susskinds "Quantum Entanglement" Lecture Series and in Lecture 1 he explains that when measuring the angle of an electron poles in lets say one axis that no matter what the ...
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1answer
61 views

Hamiltonian operator in spherical coordinates

I'm studying the hydrogen atom from a quantum mechanics perspective, but I'm having troubles understanding a step. Consider the stationary Schroedinger equation: $$\hat H \psi = E\psi$$ Let $M$ be ...
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1answer
43 views

Understanding the basic concepts of quantum mechanics using a model [duplicate]

I'm not an expert and I don't know if already exists something like the following model, but I wrote a simple (mental) model to understand the basic concepts of quantum mechanics. I want to know if ...
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1answer
63 views

Why does general relativity need space to be continuous? [duplicate]

http://www.askamathematician.com/2009/12/q-howwhy-are-quantum-mechanics-and-relativity-incompatible/ So I was reading this article because I'm new to this stuff and don't quite understand the ways in ...
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2answers
42 views

Double slit with observer?

https://www.youtube.com/watch?v=Xmq_FJd1oUQ Apologize if this is a dumb question, I'm just a kid trying to make sense of something that I'm new to. It shows the wave interference when you send a ...
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0answers
59 views

Alternatives to the Feynman Lectures [duplicate]

I wanted to get a grounding in quantum mechanics, and was directed to the Feynman lectures. I was told to start from Vol I and work my way up to Vol III, where all the quantum mechanics stuff is. As a ...
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39 views

How do I expand the state $| x \rangle$ in terms of another orthogonal basis?

In my quantum mechanics textbook it says that the relation between the basis $|x\rangle$ and $|p\rangle$ is given by: $\langle p | x \rangle = \Large \frac{e^{-ip x/ \hbar}}{\sqrt{2\pi \hbar}} \, .$ ...
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1answer
70 views

why does quantumn theory not reconcile itself with general relativity [duplicate]

Why has there not been a resolution in the gravitational effect between the two? It seems that quantum theory and Einstein disagree.
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1answer
59 views

Question about heisenberg uncertainty principle and single-slit diffraction

My question relates to this video illustrating the Heisenberg uncertainty principle. The video shows light being shot through a slit forming a spot on a screen. As the slit narrows, the width of the ...
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1answer
121 views

Why are the elements of the periodic table stable? [duplicate]

I apologize in advance for the stupid question, but I was wondering about neutron decay and elements. Taking for example one of the most simple elements, Helium. Helium is made by 2 neutrons and 2 ...
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2answers
139 views

Rigorous Mathematical Proof of the Uncertainty Principle from First Principles

While looking at an intuitive explanation for the Heisenberg Uncertainty Principle (related question below), there was a mention of an axiomatic approach to establishing the uncertainty principle. ...
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194 views

Does quantum mechanics break causality? [duplicate]

If quantum mechanics is probabilistic, there is no reason for a particle to be in one place and not the other, but particles do make up their minds... but how?
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3answers
79 views

What changes in the electrons before and after a voltage drop?

It is easy to visualize gravitational potential energy as a function of the position of height, and a change in this potential is manifested in a change in height. Further, by the work-energy theorem ...