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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Probability density for momentum in Quantum Mechanics

In a book i found the following equations: $$ \phi(k)=\frac{1}{\sqrt{2\pi}} \int_{-\infty}^\infty \Psi(x,0)e^{-ikx}dx $$ and $$ \Psi(x,t)=\frac{1}{\sqrt{2\pi}} \int_{-\infty}^\infty ...
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25 views

How to write magnetic dipole transition hamiltonian using ladder operator?

The magnetic dipole transition Hamiltonian is $\hat{H}=\frac{e}{2m_ec}\hat{\mathbf{B}}\cdot\hat{\mathbf{L}}$ How do I express it in terms of ladder operator $\hat{L}_+$, $\hat{L}_-$, and the ...
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2answers
64 views

Shimmering from heated air and the speed of light

A few months back, I was using binoculars to check if my friend was on his boat, which was around 2 to 3 km out to sea from the shoreline where I was standing. The images from, say the sail of the ...
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36 views

Ground state symmetry breaking in Bose-Hubbard model with spin-orbit coupling

The Hamiltonian for 2D Bose-Hubbard model with spin-orbit coupling on a square lattice is written as $ H = -t\sum_{\langle ij \rangle}\Psi_i^{\dagger}\Psi_j^{\vphantom{\dagger}} + ...
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47 views

Probability of Vacuum Fluctuations near Charges

A short, simple enough question, if you know about field theory, which unfortunately I don't. Are vacuum fluctuations more probable near a charge, for example an electron with negative charge? I ...
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30 views

What is the difference between the phase in molecular orbitals and the actual complex phase component of the wave function?

You often see in atomic and molecular physics texts that bonding occurs between two atomic orbitals when their wave functions are in phase. These pictures often depict the 'phase' as whether or not ...
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83 views

Problem with momentum values in a QM problem

I have the following equation of $Ψ$ around a ring (the particle is bound to move only on the ring): To visualize the state(it dies before L/2 if L=2πR): We can see from the first picture that ...
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3answers
97 views

Elementary particles that make up an atom

How many real elementary particles (not hypothetical) make up an atom or can be in an atom?
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57 views

Is this definition of orthohelium and parahelium incorrect?

"One electron is presumed to be in the ground state, the 1s state. An electron in an upper state can have spin antiparallel to the ground state electron ($S=0$, singlet state, parahelium) or ...
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2answers
40 views

Why do nuclear multipole moments of charge density vary with isotopes?

Why do some isotopes have different quadrupole/octupole moments, when these moments of charge density should be independent of mass?
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2answers
58 views

Expectation value of Hamiltonian [closed]

The Hamiltonian of a system is $H=\frac{L^2_z}{2I}+gBL_z $. The initial state is $\Psi(0)=A\sin^2\phi $. I want to find the expectation value of $H$ for $t=0.$ I think that I should express ...
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1answer
53 views

Operator in Hilbert space of a spin

I'm studying quantum mechanics with Shankar's "Principles of Quantum Mechanics" 2nd edition. I'm afraid that it might be a boring question but I can't understand the following statement (389p): We ...
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Is half-life a statistical average of variable decay times?

Is the half life of a material only accurate as long as you are still in a macroscopic regime? If I had 8 particles in a box would I observe a fluctuation in half lives, and what would occur within ...
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65 views

How could general relativity and quantum mechanics ever be combined? [duplicate]

Maybe I'm mistaken but here it's what I understand: Einstein's theories have to do with space time curvature. Whilst quantum mechanics has to do with probabilities. The solutions to the Shrodinger ...
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33 views

Does quantum mechanics have any insight into why and how photons get adsorbed into atoms? [duplicate]

Relativity holds that energy and mass are equivalent via the equation $E=mc^2$ also I know in quantum mechanics we talk about electrons jumping into bigger orbitals if they gain just the right amount ...
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32 views

Nuclear shapes and deformation

How do the experimentally measured multipole moments (static or transition) give information about the deformed nuclear shape? Since deformation is not directly observable, the only information we get ...
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1answer
76 views

Obtaining quantum Hamiltonian for charged particle from path integral formulation

I was working on Shankar 8.6.4, which is about obtaining in one dimension the Hamiltonian operator of a charged particle from the path integral formulation. First, I get the propagator over a time ...
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84 views

What was the largest object/particle tunneling observed?

What is a current record? Reference to that would be nice. and what can be expected in near future? what are the theoretical limits?
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73 views

What is this nested bracket notation?

The following is an excerpt from K. Varga's paper, Precise solution of few-body problems with stochastic variational method on correlated Gaussian basis: ...The function $θ_{LM_L}(\mathbf{x})$ in ...
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1answer
87 views

Transition from one state to another in Quantum Mechanics

I have seen other questions in this website that ask the same question, but no answer was clear enough for me. So, when we measure an electron's position we know that the wavefunction $\psi$ peaks ...
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1answer
36 views

How does Kohn's theorem demonstrate that a rotating microwave field can only connect the ground state with the cyclotron mode?

This is a follow-up question to Proof of Kohn's theorem. I am confused about a point in the answer given by @NowIGetToLearnWhatAHeadIs. It is noted that the perturbing Hamiltonian in Equation 12 ...
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56 views

Is there any quantum experiments or effects that you can do at home? [duplicate]

I have heard that you can do the double slit experiment, but is there any other experiments like particle entanglement or observer-induced state collapse?
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57 views

How long do electrons take to “decide” how to go through a circuit?

Many other people have asked how an electron decides which path to take, but no one has asked how long do they take. Is there an equation for their "uncertainty" time? Do they decide instantaneously ...
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56 views

Negative sign in rotation operator (quantum mechanics, angular momentum)

Schaum's Quantum Mechanics comes up with $$\exp((-i/\hbar)\cdot \theta \cdot{\hat{L}} \cdot {\overrightarrow{n}})$$ as the formula of the rotation operator. Other sources I see don't have the ...
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2answers
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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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Infinitesimal Rotations

Have a little question regarding infinitesimal rotations. In the Cohen Book, volumen 1, Complement B-VI, it says that the transform of a vector $\textbf{OM}$ under an infinitesimal rotation can be ...
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How asymptotically efficient is quantum state tomography of a flat qubit?

Suppose you receive $n$ copies of a qubit rotated by an unknown angle. That is to say, you're given the state: $$T(\theta) = \left(\sin(\theta) \left|0\right\rangle + \cos(\theta) ...
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1answer
49 views

does photon travels in a helical path in an optical vortex?

The wave front of the optical vortex beam is helical. Does it mean that the photon travels in a helical path? When the optical vortex beam is focused on a screen, an annular ring with dark center is ...
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1answer
54 views

De Broglie wavelength Vs Wavefunction

According to De Broglie's eqn by calculating momentum of electron in 1st orbit of hydrogen, the wavelength is itself the diameter of the atom, so what does it tell abt the wave function? In general ...
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1answer
36 views

what does interference between two decays amplitudes mean?

can anyone explain to me what does interference between two decay amplitudes mean? I'm reading about the GLW and ADS methods used to extract the CKM angle gamma they are both based on the interference ...
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1answer
46 views

Commutators and Operators [closed]

Is commutator of two operators an operator? I searched google but still got no success! I'm very curious to know the answer to this!
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2answers
33 views

On linear operators and their complex qualities

In the Principles of Quantum Mechanics, Dirac states that all linear operators $\alpha$ over our vector field (over the complex numbers) can be expressed as the sum of a real and an imaginary part ...
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1answer
48 views

How to transform the Laplacian from momentum space to coordinate space

I'm working through some quantum mechanics problems with solution sets (attempting the problems then looking at the solutions to compare), and a little part of a solution has stumped me. I'm not sure ...
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1answer
32 views

What are the characteristic of a unitary acting on a composite system?

I have a composite system AB, initially the state of the system is $|\psi\rangle_A \otimes |\phi\rangle_B$. $U$ is an operator acting on the composite system. If even after application of the operator ...
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1answer
56 views

Differentiating between Tensor Networks

I am trying to study tensor networks and their application to quantum phase transitions. However, I had a question concerning the connection between the projected entangled-pair states (PEPS) and the ...
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34 views

Why only the spin $j=\frac{1}{2}$ has relativistic wave function equation that conserves positive probability?

The Dirac wave function can be thought as a relativistic wave equation, where the solution has a positive definite norm. I know that this same equation can't be thought so seriously as a wave equation ...
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1answer
122 views

Why “textbook examples” of solutions to Schrodinger equation only deal with electrons?

Whenever studying first courses of quantum mechanics, the Schrodinger eqaution is always illustrated by an electron in some kind of a potential, and the solution (wavefunction) represents probability. ...
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3answers
111 views

Why does a violation of locality not imply a violation of relativity?

This question is closely related to: What counts as information? Taking the specific example, again, of the EPR experiment. I think everyone agrees on the following: The act of measuring the ...
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1answer
99 views

How did Schrödinger come up with his equation?

So all of the people who studied QM know the famous Schrödinger equation. I have read that it was not derived, but it is a postulate; something that is just real. Some people have tried to explain ...
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Intuition behind the solutions of the Schrodinger equations

I am learning the basic and easy first examples of the most common problems in Quantum Mechanics,and while trying to find solution to the Schrodinger equation,i find myself struggling with the ...
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What is Bell Measurement (wrt its use in quantum teleportation)?

Bell measurement is joint quantum-mechanical measurement of two qubits, so that after the measurement the two qubits will be maximally entangled. According to the answer here, this is acceptable ...
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1answer
29 views

Why should odd-ordered electric multipole moments vanish?

In the multipole expansion of the radiation field of a nuclear, it is considered that the odd-ordered poles (like electric octupole) must vanish in order to conserve parity. But there exist many ...
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1answer
30 views

How are anti-unitary operators applied?

I was reading about anti-unitary operators from Wikipedia. They give an example of an anti-unitary operator: were $K$ is complex conjugate operation. $\sigma_y$ is defined with respect to two ...
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1answer
45 views

Quantum mechanics prediction for Bremsstrahlung?

Does quantum mechanics predict the Bremsstrahlung Phenomena? I know it is predicted by classical mechanics through Maxwell's equations, but does QM predict this phenomena and how so?
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41 views

Understanding Quantum point contact

Am I correct in saying that quantum contact is : for a quantum heterostructure, by applying a voltage between two needle shaped split gate, it would deplete the electrons beneath it, therefore ...
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54 views

Double-slit experiment, dielectric material containing the two parallel slits

This is concerning the double-slit experiment. This is concerning the material containing the two parallel slits. Are there experiments where the material containing the two parallel slits -- is ...
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1answer
73 views

Why do $H$ and $L^2$ commute in spherically symmetric potential?

In this PDF document (a lecture by Shivaly Reddy, page 13), he says that $L^2$ is independent of $r$; therefore it commutes with any function of $r$. This seems related to a problem in ...
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1answer
78 views

Fiber bundle understanding of the wavefunction

Usually people say that given a wavefunction $\Psi$ although $|\Psi(\cdot, t)|^2$ is the probability density for the position random variable at time $t$, the wavefunction $\Psi$ itself has no ...
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36 views

What kind on transformations can be applied on density matrices?

Completely positive trace preserving maps ( CPTP ) transform a valid density matrix to another, then why do we only talk about unitary transformations on density matrices ( $\rho \to U\rho ...
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2answers
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Commuting observables and CSCO's

I've been looking at some basic quantum mechanics all day in an attempt to better my understanding of the subject. While going over the proof that commuting operators are compatible, I started getting ...