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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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
10 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
27 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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0answers
27 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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42 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
20 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
46 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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128 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
48 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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67 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
51 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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32 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
18 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
38 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
42 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
88 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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30 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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33 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 ...
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1answer
49 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
14 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
33 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 ...
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25 views

Difference between apply quantum gate and measure a qubit?

When you apply a quantum gate, why does the superposition state not collapse? Does this in any way intervene with the qubit as in the measurement?
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1answer
34 views

Do all quantum systems have zero point energy ?

I understand that it is possible to write an uncertainty relation between the Hamiltonian of a system and time, where the time uncertainity is defined by the amount of time it takes an arbitrary ...
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22 views

How do I find the electron confinement energies in a spherical quantum dot?

So if I've got a spherical quantum dot, we'll say it has a 10nm diameter for simplicity. This dot is a semiconductor and it has an electron with an effective mass altered by a factor of 0.2. How do I ...
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1answer
75 views

Quantum Mechanics Notation

Generally we have that $$|\psi\rangle=\int_{all space} \psi(\mathbf x)|\mathbf x\rangle d^3\mathbf x$$ and therefore $\psi(\mathbf x)=\langle\mathbf x|\psi\rangle$. When discussing the mutual ...
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1answer
29 views

Normalisation of simple wave function [on hold]

I'm currently hanging on a simple normalization of following wave function: $$\psi_1(x)=N_1\exp(-\frac{(x-a)^2}{4a^2}),$$ where $N_1$ is the normalization factor to get, and $a\in \mathbb{R}$ ...
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2answers
49 views

Classical notion of trajectory [on hold]

Why the classical notion of trajectory is meaningless in quantum mechanics? I am asking here about notion of trajectory from classical mechanics and why in quantum mechanics we cannot use it or is ...
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1answer
30 views

Using creation and annihilation operators to prove the expression for the $n$th excited state in terms of the vacuum state

How does one prove that the $n^{th}$ excited state of a quantum harmonic oscillator (QHO) can be obtained by applying the creation operator $a^{\dagger}$ $n$-times to the vacuum state $\vert ...
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1answer
42 views

Derivation of Interaction energy of Dipole - Induced Dipole Interaction

I see that the formula giving the potential (interaction) energy of a dipole and an induced dipole is $$V=-\frac{C}{r^6}$$ where $$C=\frac{\mu_1^2 \alpha'_2}{4 \pi \epsilon_0}$$ and that the formula ...
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24 views

Strong and Weak limits in Quantum Mechanics

What are strong and weak limits in Quantum Mechanics ? especially in the terms of scattering theory and Moller operators ? References to some standard book will be appreciated.
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67 views

Quantum mechanical tunneling [on hold]

Keeping extraneous ideas and postulates to a minimum, How can we explain the process of quantum-mechanical tunneling?
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1answer
46 views

How are the PPT criterion and Bell's inequality different?

Bell (1964) writes that if we assume an equivalent classical hidden variable distribution for a two-qubit state then the expectation value of the product of two observables $A$ and $B$ can be written ...
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1answer
40 views

What is the meaning of “site”?

Reading questions, I have come across a recurring notion of "site". Whilst I am able to understand the questions I am unsure as to what a "site" actually is and to what it corresponds physically. I ...
3
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1answer
49 views

Evolution of Eigenstates when two spin systems are coupled

I would like to describe the following situation: We have two spin systems: Spin 1 ($S_1$) and Spin 1/2 ($S_2$). Now imagine you somehow change their interaction so that you can finetune the ...
7
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1answer
288 views

Do electrons oscillate into muons just like electron-neutrinos into muon-neutrinos?

And if not, why? What is the difference to neutrinos oscillations?
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1answer
50 views

Eigenvectors of $p_x$ in a particular domain

Defining the $p_x$ operator for the problem of particle in a infinite well. In the book by Capri on Quantum mechanics, the domain of the operator is given by, $$ p = -i\hbar \frac{\partial ...
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1answer
22 views

Physical Significance of the Planck Density

The Planck density is the Planck mass devided by the Planck volume, approximately 1093 g/cm3. Does this quantity have any known physical relevance? The Planck mass is believed to be the smallest ...
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1answer
58 views

Commutator of fermionic operators

The fermionic creation/annihilation operators are defined by the anti-commutation relations: $$ \{a_k^{\dagger},a_q^{\dagger}\} = 0 = \{a_k,a_q \} $$ $$ \{a_k^{\dagger},a_q\} = \delta_{kq} \, .$$ I ...
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0answers
29 views

Pion decay exercise in Griffiths books

I have questions about pion decay problem. In Griffith "Introduction to Elementary Particles" 1st edition, 1987, question number 10.10 : Analyze $\pi^-$ decay as a scattering process, using the ...
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2answers
47 views

How to verify/falsify the existence of localised edge states numerically?

I have to consider a Hamiltonian given in second quantized form in real space $$H = \sum c_k^\dagger h_{kl} c_l \, ,$$ describing fermions on a 2d hypercubic lattice. The concrete form of the matrix ...
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46 views

Computing the probability density of wavefunctions

Suppose I am given a Hamiltonian operator $\hat{H}$ that satisfies the time-independent Schrödinger equation $$\hat{H} \psi = E\psi$$ I can compute energy eigenvalues and their associated ...
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Why Position & Momentum but NOT Position & Forces involved were considered in Uncertainity Principle?

Why Position and Momentum are considered in Uncertainity Principle? What I understood is that we can predict the future state of system if we know the position and momentum of all particles ...
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45 views

What does Bell's theorem rule out?

What exactly did Bell's theorem rule out? Did it rule out "locality", so we must give up and think of Copenhagen or maybe some realism theories (Bohmian for example)? ... That's how I understand ...
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2answers
63 views

Are matter waves (de Broglie) classified as transverse or longitudinal? [duplicate]

We know that waves are of two types: transverse and longitudinal, and we have studied about de Broglie waves as well, so which one of them is it? Or we have other means to classify them?
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Are there any in depth superfluid mechanic analyses of spacetime?

Has there been much work done that treats particles as vortexes in a fluid, or dark matter as bubbles in this fluid (bending space in the same way massive particles (vortexes) are observed to do, but ...
3
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MRI and precession

A lot of explanations of the quantum mechanics of MRI discuss the precession of a proton in an external magnetic field, for example here: http://www.physicscentral.com/explore/action/mri.cfm Doing ...
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1answer
34 views

The Sturm-Liouville equations, the Schrodinger equation and the wave equation

I heard in a online quantum mechanics lecture that Schrödinger equation is an instance of the Sturm-Liouville equation and that is the super position of its stationary states gives the most general ...