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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Dirac field and stress-energy tensor density

I read somewhere that stress-energy tensor density is a symmetric tensor. But if I take the Dirac Field tensor: $$T^{\mu \nu}=i \psi^\dagger \gamma^0 \gamma^\mu \partial^\nu \psi $$ How could I ...
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122 views

Practical example of stabilizer codes

Given the Steane code $$ \left|0\right\rangle_L \equiv \frac{1}{\sqrt{8}}(\left|0000000\right\rangle + \left|1010101\right\rangle + \left|0110011\right\rangle + \left|1100110\right\rangle + ...
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3answers
5k views

Average Energy of the Quantum Harmonic Oscillator

In Griffiths, the average potential energy for the quantum harmonic oscillator is given as $$\langle V\rangle~=~\frac{1}{2}\hbar \omega(n+\frac{1}{2}).$$ Is the potential energy of the quantum ...
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353 views

A simple question on $SU(2)$ gauge transformations in Wen's papers on projective symmetry group (PSG)?

Recently I am studying the projective symmetry group (PSG) and the associated concept of quantum order first proposed by prof.Wen. In Wen's paper, see the last line of Eq.(8), the local SU(2) gauge ...
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255 views

Unitary Operator apply to Entangled vector

I am trying of resolve this exercise: Show that if $|\psi \rangle$ is an entangled state of two Qbits, then the application of a unitary operator of the form $U_1 \otimes U_2$ necessarily generates an ...
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4k views

Energies and numbers of bound states in finite potential well

Hello I understand how to approach finite potential well (I learned a lot in my other topic here). However i am disturbed by equation which describes number of states $N$ for a finite potential well ( ...
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227 views

2 following gates, permutation matrix

I have a circuit that has 4 wires and 2 following each other Toffoli gates. I have permutation matrix for each Toffoli gate (A and B). Do I have to multiply that 2 matrices to get the entire ...
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509 views

Two Qubit problem

A two-qubit system was originally in the state $ \frac{3}{4}|00\rangle-\frac{\sqrt{5}}{4}|01\rangle+\frac{1}{4}|10\rangle-\frac{1}{4}|11\rangle $ , and then we measured the first qubit to ...
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872 views

Wave functions for three identical fermions

I would like to express the wave functions for three identical particles, each with orbital angular momentum $L=1$ and spin angular momentum $S=1/2$, in terms of single-particle wave functions. In ...
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153 views

Noise spectrum of two systems and interacting Hamiltonian

I've been discovering recently the concept of noise spectrum, defined as: $$S_{xx}[\omega] = \int dt \langle x(t)x(0)\rangle \text{e}^{-i\omega t}$$ Roughly the Fourrier transform of the two-point ...
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967 views

Force exerted on potential wall

A particle bound in an infinite potential wall at $x=0$ will apply a force on the wall. For a plane wave and imagining it as a fluid bouncing off the reflection wall at $x=0$, find the force in terms ...
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320 views

Complete set and Klein-Gordon equation

In http://www.physics.ucdavis.edu/~cheng/teaching/230A-s07/rqm2_rev.pdf, it says that when there is some external potential, the Klein-Gordon equation is altered, and it says the following: The ...
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687 views

Matrix mechanics for those with wave mechanics background

Just curious: Is there any book or resource that teaches matrix mechanics (quantum mechanics) only without wave mechanics stuff - meaning that the book assumes wave mechanics background.
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651 views

Where does the “borrowed energy” come from in Alpha decay?

I was also thinking about the uncertainty principle in regards with energy & time. The question of something like: Alpha tunneling out of the nucleus is where this can be invoked, but having an ...
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what is expectation values of this anti-commutator?

what is expectation values of this anti-commutator? $$\langle \{ \Delta \hat x,\Delta \hat p\} \rangle$$ where the $\Delta \hat p=\hat p-\langle \hat p \rangle$ and $\hat p$ is momentum operator and ...
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644 views

How Represent Waves via Complex Numbers?

i try to finished my thesis, (Just have a problem with the wave mechanics) this is wave function: $$\Psi(\vec x, t)=A\exp{i(\phi+\vec k.\vec x-\omega t)}$$ In mathematics, the symbol $i$ is ...
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77 views

shouldn't we add the oscillating terms into Bohr-Sommerfeld quantization formula

shouldn't be the quantization formula (in one dimension) equal to $ N_{smooth}(E)+N_{osc}(E) = \oint_{C}p.dq $ ?? where the Oscillating term is just the correction from Gutzwiller trace formula or a ...
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1k views

Questions on wave-particle duality

Wave-particle duality states that a particle has both wave properties and particle properties when one is not observing it. 1) What is an observer? Need it be anything living or can other particles ...
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151 views

What is an isoscalar factor?

I need to find a definition for "the isoscalar factors of 3j-symbols for the restriction $SO(n)\supset SO(n-1)$...denoted by brackets with a composite subscript $(n: n-1)$..." They are given as: $$ ...
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5answers
951 views

Observable: possible outcome of measurement vs (linear) transformation

One of the postulates of quantum mechanics is that every physical observable corresponds to a Hermitian operator $H$, that the possible outcomes of the measurements are eigenvalues of the operator, ...
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736 views

Atom Theory vs Quantum Physics

This never really occurred to me until now, so maybe it does not categorize as a really important question, but, according to Quantum Mechanics, anything that is not observed exists as a probability ...
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2answers
256 views

Reconstruction of information stored in an evaporating black hole from the emission spectrum?

For simple setups, where the radiation field deviates not too far from thermodynamic equilibrium (< 10 %), corrections to the Planckian thermal emission spectrum can be calculated (and measured) ...
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76 views

Decrease of uncertainty of momentum with increase of width of infinite well in QM(intuition)

Why does the uncertainty in the momentum decrease with the increase of the width for an energy eigenstate in the classic problem if the infinite well in Quantum Mechanics? I have worked out the ...
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64 views

Is this correct? $Tr_{B}(U_{AB}(I_A\otimes \rho_B)U_{AB}^{+})=I_A$

A composite system AB, its initial state is a product state of A and B given by $(I_A\otimes \rho_B)$ (A in a completely mixed state). The composite system undergoes a unitary operation $U_{AB}$. My ...
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66 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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69 views

Why doesn't the quantum eraser violate the no-deletion theorem?

In the quantum eraser experiment and its variants, you basically have a double slit experiment, where you detect which slit the photon went through, but then forget this information. My question is, ...
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108 views

How many eigenstates for four (non-identical) spin 1/2 particles? [closed]

Question Consider a system of four non-identical spin 1/2 particles. Find the possible values for the total spin and state the number of eigenstates for each of these. Attempt So I coupled S1 and ...
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90 views

Difference for boundary condition, particle in a box

When solving the simple problem of a free particle in a box of volume $V = L^3$, we can impose either periodic boundary conditions $\psi(0) = \psi(L)$ and $\psi '(0)= \psi'(L)$ either strict boundary ...
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170 views

Superposition of waves with different initial phase in Quantum Mechanics [closed]

In Quantum Mechanics, if a particle's state is a superposition of many states, then we say that its position is well-defined (by the Heisenberg uncertainty principle, because here we have ill-defined ...
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76 views

derivation qm canonical ensemble

In classical mechanics the canonical ensemble can be derived from the microcanonical ensemble of two systems in weak interaction. Is a similar thing possible in quantum mechanics? Is there any good ...
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173 views

What would be the Slater's determinant representation for an excited state?

Setup Introducing this spinorbital notation: \begin{align} \Psi_1=\chi_{(r1)}\alpha_{(\omega1)} = 1 \\ \Psi_1=\chi_{(r1)}\beta_{(\omega1)} = \bar{1} \end{align} and the Slater's determinant, for ...
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128 views

multiverse fabric of reality

Source-"fabric of reality"- author d. deutsch - his contention, as I understand it, is that quantum interference is caused by "almost, but not identical quite quantum entities" , e.g. electrons, from ...
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64 views

What is the correct way to treat operators that has “time” in QM? [duplicate]

I don't know if this question has already been resolved but considering that $i\hbar\partial_t$ is the energy operator, and $\partial^2_t$ is the waves operator (or helmholtz), I can't accept that $t$ ...
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385 views

Does time reversal symmetry hold for (kitaev model) 1D spinless $p-$ wave superconductor?

The hamiltonian 1D spinlesss p wave superconductor can be written as $$ H=\sum_k \phi_k^\dagger \begin{pmatrix} \xi(k) & 2i\Delta \sin(k)\\ -2i\Delta \sin(k ) & -\xi(k)\end{pmatrix}\phi_k $$ ...
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What's the Cause of Quantum Entanglement? [duplicate]

What is the cause of quantum entanglement? When two particles become entangled what property of them basically changes as to establish a link between them and how the information is exchanged between ...
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302 views

Pressure in Harmonic Oscillation

Classical Harmonic oscillator's energy depends on temperature as it equals $k_B$$T/2$. However, quantum harmonic oscillator energy is $(n+1/2)hf$. So, when T=0, quantum predicts motion. I have been ...
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226 views

What is matter made of in the light of Quantum Mechanics? [closed]

I've always wondered what matter (particles, force particles, etc.) was actually made of considering the fact that quantum mechanics has shown us that particles can actually act as a probabilistic ...
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32 views

How to write “postselection” operator?

Suppose, I wish to know an operator, which eigenvalue is 1 if state is exactly F and 0 ...
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152 views

Quantum Mechanical States

What can be the precise answer to the question that Quantum states are complex and infinite dimensional. Why is this so? Is it because they belong to the complex Hilbert space? Even if they ...
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3answers
448 views

Solving the Schrödinger equation where the initial wave function is an energy eigenfunction

I was watching Allan Adams' lecture on energy eigenfunctions, and there's one part (around 43 minutes into the lecture) that confuses me. Suppose we have the initial wave function $\Psi (x,0)$ such ...
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2answers
164 views

Representations in quantum mechanics [closed]

This might be a very simple question. I just want someone to point me the right direction to understand things like this: $$ \langle x|x'\rangle=\delta(x-x') \\ \psi(x)=\langle x|\psi\rangle \\ ...
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214 views

How do we measure a quantum system properties? (length, mass and time) [closed]

How do we measure a quantum particle properties? (length, mass and time)
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163 views

At what point does everything become nothing?

I understand that the universe, which I'll call "everything", is expanding and it used to be much smaller. But I keep hearing assertions about a universe coming from nothing. If you rolled the clock ...
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112 views

Question about a finite time interval step in the derivation of the Feynman path integral in Sakurai

This may be a possible errata but Sakurai (pp 126 in the 2nd Edition) states that starting with $$S = \int dt \,\,\scr{L_{\mathrm{classical}}}$$ Looking at a finite-time-interval of the action: ...
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666 views

Probability current density : Isn't there something wrong with this proof?

Is there something wrong with the following proof (see below)? To me, it seems like the third line should show $$\frac{dP_{ab}}{dt}=-\int_a^b \frac{\partial}{\partial t}J(x,t)dx$$ Am I missing ...
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345 views

Hardy's Theorem

https://perimeterinstitute.ca/psi_portal/sites/perimeterinstitute.ca.psi_portal/files/hardyphysrevlett.68.2981.pdf Some researchers in Bohmian Mechanics have hoped to make the theory Lorentz ...
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394 views

Quantum Entanglement - Measuring Twice

In the answer here and on the wiki article and many other articles it is mentioned that if one of 2 entangled particles is measured their state collapses according to the Copenhagen interpretation. ...
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Dr. Pierre-Marie Robitaille: On the Validity of Kirchhoff's Law

Lately I've been researching about the black-body spectrum and the historical development of Planck's Law. I mainly wanted to understand a little bit more why many different objects (Stars, Hot ...
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2answers
204 views

Linearity in Quantum Mechanics that make superposition possible

As a beginner in QM, all the video lectures that i have seen talk about superposing wave functions in order to get $\psi$. But from what i know from linear algebra, the system must be linear in order ...
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135 views

In Quantum mechanics, what is realism? [closed]

Some interpretations of QM are realist and some are anti-realist. But, it is the idea that something exists before it is measured, correct?