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Questions tagged [quantum-mechanics]

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 quantum-field-...

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22 views

Hyperfine structure of hydrogen

I have an expression $H=a \vec{I} \vec{S}$ which is a leading term in Hamiltonian for the hyperfine structure of p-states in hydrogen, but I don't really understand it. By Wigner-Eckart, hyperfine ...
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21 views

quantum mechanics and calculations for small spacetime regions

What is your position on one of Feynman's statements regarding the nature of Quantum Mechanics and the infinite amount of calculations needed to estimate a quantum property of a very small segment of ...
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1answer
26 views

Bose Einstein Condensate

In Bose Einstein condensate photons stop moving, but with reference to what frame of reference? Photons move at constant speed in all reference frames so what happens to Maxwell equations at zero ...
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1answer
45 views

Getting the density of states for photons

I know that the density of states $g(\epsilon)d\epsilon$ is the number of states in the energy range $[\epsilon, \epsilon + d\epsilon]$. I considered a system of non-interacting free photons in 3 ...
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21 views

QED Feynman diagrams for 3rd order processes

I'm trying to draw the leading order, tree level diagrams for the two closely related QED processes: $$\gamma + e^{-} \rightarrow e^{-} + \mu^{+} + \mu{-}$$ $$\gamma + e^{-} \rightarrow e^{-} + e^{+}...
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4answers
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What is the proof of entanglement?

Really I know entanglement exists, but what I have never found is experimental evidence that measuring one entangled particle causes the state of the other entangled particle to change, rather than ...
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1answer
33 views

2$\pi$ Rotation on integer vs half-integer spin states

I want to know how to get the following result: $$ e^{-i2\pi J_y / \hbar}|j, m\rangle = (-1)^{2j}|j, m\rangle $$ for an arbitrary spin state $|j, m \rangle$. What I've tried is to expand the ...
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73 views

Is the ground state a Schrödinger cat state?

Consider the following Bose-Hubbard Hamiltonian which describes a Bose-Einstein condensate confined in a two-well potential: $$ H= -T(a_L^\dagger a_R + a_L a_R^\dagger ) + \frac{U}{2}(n_L^2+n_R^2-...
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Instrumentalism: rotating a waveplate vs changing from one linear opeartor to another

When doing simple quantum experiments, like say analyzing polarization of an optical beam, we often find ourselves rotating waveplates. In our lab, there is a morphism of our apparatus that maps the ...
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1answer
47 views

How does this term $e^{i\Phi_0}$ get removed in bloch sphere equation?

A qubit can be represented in the form of $$|\psi\rangle=\alpha|0⟩+\beta|1\rangle$$ where $\alpha$ and $\beta$ are complex numbers. Or a complex number can be expressed by $R e^{i\Phi_0}$. so the ...
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35 views

SupaComplicated Schrodinger's Cat [on hold]

A simple beginning Okay, so we have a Schrodinger's cat. You know, a cat, a box, some radioactive material, a Geiger counter, a flask with a poison, and a hammer is the traditional setup. This cat, ...
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53 views

Simultaneous measurements in Quantum Mechanics

In the notes I am using, it states that if two observables A and B are measured simultaneously, then the measurement of A does not affect the measurement of B, and vice versa. However, why does the ...
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0answers
19 views

self-adjoint extension of the momentum operator in an infinitely deep potential

Theta parameter arises when calculating self adjoint extensions of the momentum operator of a particle in an infinnitely deep potential, what does this means physically?
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0answers
53 views

Ising model with quantum magnetic field

Hamiltonian of the Ising model with an external magnetic field is written as $$H=-J\sum_{\langle i,j \rangle} s_i s_j + h\sum_j s_j$$ where $J$ is nearest neighbor coupling constant and $h$ is the ...
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2answers
38 views

Altering Young's double slit experiment due to observation

The interface pattern on the screen is altered due to our observation, but how could this happen, as we have been watching it since we started the experiment? Is there any other meaning of '...
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0answers
41 views

Can many worlds interpretation have universes with different laws?

The Many Worlds Interpretation of quantum mechanics is classified by Max Tegmark as a level-3 multiverse hypothesis. This means that in the universes that it will predict, there could be different ...
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2answers
116 views

Is this actually the rigorous definition of the path integral in Quantum Mechanics?

Let a quantum system with a single degree of freedom be given. We want to define the path integral so that we get the representation for the propagator as $$\langle q' |e^{-iHT}|q\rangle=\int_{x(a)=...
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28 views

Amplitude of a wave: will it be an overlap of two waves or is there another reason?

For a wave with initial conditions and with a velocity = 1.00 m / s the following graph was obtained: The spatial domain is [0; 50] m and the time domain is [0, 50] s. The wave reaches the boundary ...
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14 views

Ising to QUBO mapping for quantum annealing

I'm trying to solve an optimisation problem by simulating quantum annealing using the path-integral Monte Carlo Metropolis approach. So far I have formulated the problem as an Ising model with the ...
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0answers
22 views

Can you use the quantum eraser experiment to send messages the past?

Full disclosure, I'm just a noobie watching YouTube. In the quantum eraser experiment you can observe the interference pattern if you erase the information on whether what you're observing is a wave ...
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2answers
50 views

The allowed energies of 3D harmonic oscillator [on hold]

I'm trying to calculate the allowed energies of each state for 3D harmonic oscillator. $$ E_n = (n_x+\textstyle\frac{1}{2})\hbar \omega_x+ (n_y+\textstyle\frac{1}{2})\hbar\omega_y+ (n_z+\textstyle\...
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1answer
60 views

Is spin 1 described by $SO(3)$ or $SU(2)$ [duplicate]

What spin is described by which rotation group? I always only find information about spin-1/2
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0answers
19 views

How is the squared norm of a tensor product in bra-ket notation calculated? [on hold]

How is the squared norm of a tensor product in bra-ket notation calculated? What is the right notation, how can it be written out?
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38 views

If $λn=(1−z)z^n $, where $n=0,1,2,3…$ Range of $z$ is $0<z<1$. How we have defined this rang of $z$? [on hold]

For bipartite system, wave function of system can be written as $\sum_{n} \sqrt{\lambda_n} |n \rangle_a |n\rangle_b $ where $\lambda_n $ is schmidt coeffeicient and $|n\rangle_a$, $|n\rangle_b$ are ...
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1answer
52 views

Physical significance of no self-adjoint momentum operator on half line?

I am watching a quantum mechanics lecture by professor Schuller. He mentioned that there does not exist any self-adjoint momentum operator defined on the half line. What is the physical significance ...
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1answer
22 views

charge particle collisions

If a lithium +1 cation falls toward a fluorine -1 anion, slowly in vacuum, can they find a stable 'orbital'? If not an 'orbital' will they form some kind of stable two-body linear oscillator?
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When electron falls in the jungle and there's no observer, does it emits light? [on hold]

I'm trying to make sense of how observations can affect how small things behave, imagine countless electrons accelerating toward the ground my question is would the jungle glows when nobody is there ...
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0answers
53 views

Can we ever “measure” a quantum field at a given point?

In quantum field theory, all particles are "excitations" of their corresponding fields. Is it possible to somehow "measure" the "value" of such quantum fields at any point in the space (like what is ...
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2answers
44 views

Proving the raising and lowering of the raising and lowering operator

I am given a written proof of $\hat A^{\dagger}[u_n] = \sqrt{n+1} \ u_{n+1}$, and from it, and told to similarly prove $\hat A[u_n] = \sqrt{n} \ u_{n-1}$. However, in the written proof for $\hat A^{\...
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0answers
56 views

Approximate probability of a person's wavefunction collapsing to the moon?

As a sort of introductory concept to quantum mechanics, I've heard many explain that there's a small but nonzero probability of unlikely events happening: your hand quantum tunnels through the desk, ...
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2answers
70 views

Should Hamiltonians in quantum field theory be linear operators?

The usual structure of quantum mechanics imposes that Hamiltonians are linear operators. I am not sure if this really holds in quantum field theory. Do non-linear Hamiltonian operators really make ...
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1answer
78 views

What does Ehrenfest's theorem actually mean?

I am told that Ehrenfest's theorem, applied to a physical observable $\hat A$, is: $$\frac{d\langle\hat A\rangle}{dt}= \frac{i}{\bar h}\langle[\hat H,\hat A]\rangle$$ I don't understand how to use ...
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1answer
25 views

Time dependence of expectation value $\hat O$ if $\frac{\partial \hat O}{\partial t} = 0$

I am given the following derivation in my lectures: $$\frac{\partial}{\partial t} \langle \hat O \rangle = \frac{\partial}{\partial t}\int_{-\infty}^{\infty} \psi^* \hat O \ \psi \ dx$$ $$\implies ...
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0answers
14 views

Zero momentum in Non relativistic Quantum Mechanics and about Dirac matrices

In relativistic quantum mechanics, we can solve the Dirac's equation with an added condition that the momentum of the particle is $0$. However, such independence isn't provided by the Schrodinger's ...
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33 views

Why do the matrix elements of an operator correspond to the Fourier components of the observable in Heisenberg's Matrix Mechanics?

It is well-known that Heisenberg $a$ began developing his Matrix Mechanics by creating matrix components $$A(n,n-a,t)=A(n,n-a)e^{i\omega(n,n-a)t}$$ or $$A_{nm}(t)=A_{nm}e^{\frac{i}{\hbar}\omega(nm)t}$$...
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Use the annihilation and creation operators to calculate for a one-dimensional harmonic oscillator? [on hold]

Use the annihilation and creation operators to calculate for a one-dimensional harmonic oscillator the following the energy eigenvalues the expectation of momentum in the nth eigen state ...
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0answers
15 views

Realization and implication of a qutrit/qudit [on hold]

How can one realize a qutrit/qudit on a classical machine? How can it hold classical data encoded to quatum values?
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1answer
36 views

Proving equivalence of first and second quantisation (Pathria's way)

I'm trying to solve problem 11.1 form Pathria R. K. & Beale P. D. - Statistical mechanics book (the hyperlink will get you straight to the page of the problem). The point (b) is to show the ...
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1answer
33 views

Couplings in the SYK model

I have read several times by now that the couplings in the SYK model are drawn randomly from a gaussian distribution. I was wondering what exactly is meant by that. To elaborate, when I compute an ...
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0answers
52 views

Problems on perturbation theory with spin

Problems on perturbation theory with spin (solve all perturbations up to only its first-order approximation): Taking into account the relativistic correction of electron kinetic energy and spin-orbit ...
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0answers
42 views

Topological Thouless pumping

I can't understand why the number of electrons pumped per cycle of a quantum pump is protected topologically. As for me this number is an integer in any case, because the number of electrons in ...
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0answers
40 views

Learning quantum mechanics with a strong mathematics background [on hold]

Quick pedagogical question. If one were to have a substantial mathematics background prior to taking a undergraduate physics course in quantum mechanics, (say Grad. Real Analysis, Algebra, ...
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0answers
21 views

Is the basis of the occupation numbers of bosonic system orthonormal?

I am interested in the calculation of a correlation function in the Fock space of a system of $N$ bosons. As a trace it would be convenient for me to sum over the elements of the occupation numbers ...
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3answers
44 views

In what conditions we can take ground state energy $E_0$ equal to zero?

Like in 3D harmonic oscillator , $E_m = {h} \omega {(m_x +m_y + m_z + 3/2)}$, At ground state energy $m=0$ and $ E_m = h \omega(3/2)$. While discussing Bose-Einstein condensation, for calculations we ...
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1answer
70 views

Is this a “good enough” statement of Wigner's theorem from Quantum Mechanics?

I posted this on math StackExchange and got no replies, so I'm trying my luck here! I'm a fourth year physics and math student who is writing up a report on some quantum mechanical symmetries and ...
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1answer
42 views

Matrix representation composite system

I am considering an assignment involving the Hubbard model. A state is given by $|\Phi\rangle=-|2\uparrow1\downarrow\rangle-|1\uparrow2\downarrow\rangle$ where particle 1 and 2 are electrons. The ...
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How do you work out the de broglie wavelength of $C_{10}H_{10}Br_2$? [on hold]

I've got the molecule given in the title, it's at 800K and I need to work out the de broglie wavelength in order to set up a (theoretical) double slit experiment. I've used the equation $E = \frac ...
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0answers
27 views

Effective number operator [on hold]

Can we use "effective" number operator in sense of average numbers or mean occupation number of a state. Like we use effective number operator $ \langle \hat{n} \rangle $ to count number of particles ...
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1answer
33 views

What is physical meaning of state getting by acting of Hermitian operator to non-eigenstate?

The definition of an operator is $$ \hat{Q}\left|\Psi\right> = \left|\Phi\right>, $$ the thing that convert one state vector $\left|\Psi\right>$ to another $\left|\Phi\right>$. For ...
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0answers
40 views

Is spin entanglement conserved in a gravitational field?

Imagine a photon decaying into an electron-positron pair. Which have entanglement such that one is "up" and one is "down". There are a few mini black holes near by so that one of the electrons ...