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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can one distinguish between superposition with randomized phase and classical probability?(an experiment)

I hope that the following experiment will help me understand the topic better. Let's say my friend is sending me photons via two channels and he is doing it in one of the following two ways: he is ...
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15 views

Resources for introductory quantum statistical mechanics

I am currently struggling to understand my basic introductory course on quantum statistical mechanics and I have done a basic course on single particle quantum mechanics. I was wondering whether ...
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26 views

Summing over quantum states

For a system of $N$ identical particles we deal in quantum mechanics with wave functions $\langle \{\mathbf{r}_i \} \mid \Psi \rangle=\Psi(\mathbf{r}_1,\dots,\mathbf{r}_N)$ from which determine the ...
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1answer
41 views

Why is the position space free particle wavefunction a function of momentum?

This is one of those little things that has always confused me. If someone said to you "in quantum mechanics, the eigenfunctions of a free particle are $\exp(ipx/\hbar)$" how would you know that ...
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2answers
210 views

Double slit experiment with animals as observers

I was searching about the double slit experiment, reading and watching videos, etc. If I understood correctly, when they try to measure the photon it turns into particle. On the Youtube video ...
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1answer
22 views

Necessary and sufficient conditions for a function to be the Wigner function of state

For any quantum state defined with a continuous position, the Wigner function is a quasiprobability distribution on phase space. It has many properties, such as that its marginal are probability ...
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33 views

Infinite Energies of a particle in a rectangular box

For a particle trapped inside a rectangular box of side lengths $l_x$ $l_y$ and $l_z$, the energies are ...
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1answer
37 views

Spin of a particle (Quantum Mechanics)

Why the intrinsic spin cannot be expressed in terms of polar vectors or the orbital variables $\bf r$ and $\bf p$? Or, why do we need matrix representation for Spin?
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1answer
44 views

Why is it “disconcerting” if the components of an operator do not commute?

A symmetrized operator is given by $$\hat{R}=\frac{1}{2\hat{H}}\hat{N}+\hat{N}\frac{1}{2\hat{H}}.$$ With $\hat{H}$ the Hamiltonian and $\hat{N}$ the first moment of energy. The defined $\hat{R}$ is ...
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57 views

Where does an LED use energy other than emitting light?

I have a quantum formula describing what kind of photon should be emitted by an LED depending on its voltage. Of course the colour is depending on the material, but every type of LED also needs its ...
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3answers
372 views

What is meant by the term “single particle state”

In a lot of quantum mechanics lecture notes I've read the author introduces the notion of a so-called single-particle state when discussing non-interacting (or weakly interacting) particles, but none ...
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1answer
50 views

How I can launch light into PM fiber

A polarization maintaining fiber preserves the linear polarization of the light at the output, the light at the input must be linear polarized to see signal at the photodetector... However I can't see ...
3
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1answer
41 views

Cayley transform to von Neumann theorem

Self-ajointness of an operator can be found using the Cayley transform of the operator, if its unitary, $$ U = (A - i I)(A + i I)^{-1} $$ From this we can go about finding the deficiency subspaces ...
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53 views

Normalizing 3-Dimensional Wave Function [on hold]

How do you normalize a wave function in three dimensions with spherical coordinates?
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1answer
42 views

Is the superconducting current made up of Cooper pairs?

Inside the superconductor it should be $\mu_0\mathbf{j} = \mathbf{\nabla} \times \mathbf{B} = 0$, since B is 0 due to the Messner effect. This means that the current is carried by the surface. But ...
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37 views

Questions About The Delayed Choice Quantum Eraser Experiment

from wikipedia: http://en.wikipedia.org/wiki/Delayed_choice_quantum_eraser (4/20/2015) From the wikipedia article The experimental setup, described in detail in Kim et al.,1 is illustrated in ...
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1answer
47 views

Evolution operator for “blending” a pair of eigenstates

Consider a measurement operator ("observable") $\hat O$ which has ("a spectrum of") only two distinct eigenvectors; formally $$\hat O |\bullet\rangle := r_{\bullet}~|\bullet\rangle, \qquad \hat O ...
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25 views

Free particle scattering in 2D using polar coordinates

The free particle hamiltonian commutes with the angular momentum operator L and Lz, so we can use a spherical wave basis instead of the regular plane-wave basis |k>, using spherical Bessel function ...
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26 views

What is the largest atom with a reliable configuration-interaction (CI) calculation?

The simplest approximation for calculating the ground state of an atom is the Hartree-Fock approximation. To get accurate result for the ground state energy, one has to do configuration-interaction ...
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1answer
56 views

Given state cannot be written as a linear combination of pure states

Ok. This is just a numerical example to be better understood. If I am given a state let's say $\left(\begin{matrix}1\\1\\0\end{matrix}\right)$ of a H matrix let say ...
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26 views

Unanswered Questions in Quantum Phase Transitions [on hold]

What are some of the biggest unanswered questions/unexplored areas in the study of theoretical quantum phase transitions? In particular, how are people using the AdS/CFT correspondence to understand ...
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27 views
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47 views

Unitary evolution operator

Assume we have a system in a state $\psi$ that is a superposition of eigenvectors of some observable $A$. Now we make a measurement of the observable $A$; the state after the measurement $\phi$ is a ...
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2answers
55 views

Time dependent Hamiltonian and Gauge invariance

In general, in quantum mechanics we can prove probability current or the Schrodinger equation and other quantities are gauge invariant. However, the Hamiltonian isn't gauge invariant. Under a gauge ...
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1answer
68 views

Perturbations in linear response theory

I've been working on applications of linear response theory to condensed matter systems, and I've got quite far into the literature on the subject. However, there is an identity which seems to be ...
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1answer
52 views

What really is the self-adjoint extension?

Going through the Quantum mechanics book by Capri, am time and again held with some stupid doubts on this topic of self-adjointness. We have for the momentum operator in finite domain, $$ p = ...
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1answer
37 views

What is the definition of a qubit and a copy/clone of a qubit?

A qubit with state $|\psi \rangle =\alpha|0\rangle + \beta|1\rangle$ is defined as : if we have infinite copies of $|\psi \rangle$ and measure them all in the basis $\{|0\rangle,|1\rangle\}$ then ...
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1answer
19 views

Is the current vs. frequency graph hyperbolic for the photoelectric effect?

Concerning the photoelectric effect: When the intensity and applied voltage are both constant, then the current is inversely proportional to frequency $f$ (above threshold frequency). If we increase ...
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1answer
34 views

Methods to distinguish between pure/mixed states and entangled/separable states

I'm a little confused about how we can distinguish between pure/mixed states and entangled/separable states and I would really appreciate some help! I understand a density operator $\rho$ represents ...
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33 views

What's the quantization of a Hamiltonian? [on hold]

Suppose Hamiltonian of a conservative system in classical mechanics is $$H~=~\omega xp,$$ where $\omega $ is a constant and $x$ and $p$ are the position and momentum respectively. What is the ...
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63 views

Phenomena in the intersection of general relativity and quantum mechanics

I am looking for physical phenomena that have aspects involving both general relativity and quantum mechanics. The only example I know is Hawking radiation. While black holes are objects that cannot ...
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2answers
27 views

What the wave function looks of a particle in the infinite square well looks like after collapse for measurements of position and energy

Consider a particle in a the infinite square well from x=0 to x=L. At t=to, I make a measurement of position and get x=L/2. What is the resulting wave function at t=to? My understanding, from reading, ...
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1answer
54 views

Quantum state of a system after measurements with non-commutative operators

a) Assume two operators $A$ and $B$. 1) Assume $$[A,B]=0 $$ and $$ ψ= \sum c_n u_n ~~~~\text a~ wavefunction~ describing~ the~ state~ of~ the~ system $$ with $$Aψ=a_n u_n $$ $$Bψ=b_n u_n$$ If we ...
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2answers
141 views

How to interpret single photon interference when the two possible paths are different in length?

Here is my question. I struggle with the definition of single photon interference. Let’s assume we have a Michelson interferometer and the interference pattern we observe is a single photon result, ...
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1answer
50 views

Normalisation of a wavefunction [on hold]

If the system if found in the state: $$\psi=\sqrt{\frac{1}{2\pi}}(\frac1{\sqrt3}e^{-i3\phi}+ce^{-i4\phi})$$ what value of $c$ normalizes the wavefunction? Clearly: $$\int_0^{2\pi}\psi^*\psi ...
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69 views

Schrödinger Equation [on hold]

Thank you for putting my question on hold. If you will allow me a few days, beyond this weekend, to adequately rephrase the question. I need the time to find a local physicst/math professor to aid ...
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1answer
55 views

Probability of finding particle in infinite square well, displaced walls

Initially a quantum particle moves in a one-dimensional well ($x$-axis) from $-a$ to $ a$, $ V = \infty $ outside and $ V = 0 $ inside the well. So initially, the wave-function $$ \psi_0 = ...
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1answer
36 views

System of two harmonic oscillators and its quantum partition function

Consider a system of two harmonic oscillators with different frequencies $\omega_1,\omega_2$ and masses $m_1,m_2$ so the hamiltonian is $$\mathcal{H}(p_1,q_1;p_2,q_2)=\sum_{i=1}^2 ...
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1answer
21 views

Ground state wave function of Symmetric potentials

Why shouldn't the groundstate wavefunction for symmetric potentials vanish at the origin?
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1answer
41 views

Showing existence of negative temperature for a quantum system

It may be shown that the partition function for a quantum system containing N distinguishable particles each of which has energy state $\epsilon_1$ and $\epsilon_2$ is given by ...
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1answer
44 views

About states, observables and the wave functional interpretation in QFT with gauge fields

First of all, I'm a mathematician, so forgive me for my possible trivial mistakes and poor knowledge of physics. In a QFT, we just start with a field (scalar, vectorial, sponsorial, gauge etc), so I ...
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31 views

Quantum Mechanics for 1D box [on hold]

For particle in a box with mass $M$ length $L$,assume $\Delta x=L$. Assume further that $\Delta p_{min}=\langle p^2\rangle^{1/2}$.Use the uncertainty principle to obtain an estimate of the energy of ...
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2answers
92 views

Calculating quantum partition functions

...By quantizing we the get the following Hamiltonian operator $$\hat{H}=\sum_{\mathbf{k}}\hbar \omega(\mathbf{k})\left(\hat{n}(\mathbf{k})+\frac{1}{2} \right)$$ where ...
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32 views

How does a Bell measurement physically look like?

I do know how Bell states look like. They can be distinguished by doing a Bell measurement. A measurement has 4 possible outcomes (as there are 4 states, which form orthonormal basis). However I have ...
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3answers
68 views

Constants of motion in quantum mechanics

What is the meaning of a constant of motion in quantum mechanics (an observable-operator that commutes with the Hamiltonian) in contrary with classical mechanics?
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34 views

I have a problem with the variational method approximation in quantum mechanics. Is my issue valid, or am I misunderstanding something?

The variational method for approximating the ground state of a Hamiltonian $H$ by providing a lower bound is simple enough. If we construct any test wave function $|\bar{0}\rangle$ then the claim is ...
4
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1answer
60 views

Representations of Lie group symmetries on Hilbert space

I have some troubles understanding Hilbert representations for (eg) the standard free quantum particle On the one hand, we can represent Heisenberg algebra [Xi,Pj]= i delta ij on the space of square ...
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0answers
20 views

How does the Wigner-Eckart theorem rule Multipole Expansion?

I am wondering why a spin-S particle have only the term up to $k=2S$ in his multipole expansion ? It seems that the Wigner-Eckart theorem shows the relation between spin and multipole expansion but I ...
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1answer
34 views

Importance of bound states

While solving a potential well problem we get scattering states and bound states (if exist). Number of the bound states we get depends on the potential profile. What I want to ask is, what is the ...
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1answer
51 views

Do subatomic particles have dimensions?

We know atoms are mostly "made" out of empty space, so the nucleus and all the subatomic particle are very small in compared to the magnitude of the atoms. We also know that atoms are incredibly ...