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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68 views

Slit width for minimum spot size in electron slit diffraction if involving uncertainity principle

I don't believe the following is an accurate description of the physical but a homework problem to help understanding. A beam of electron of energy 0.025 eV moving along x-direction, passes ...
2
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1answer
39 views

Everyone calls Electromagnetic Induced Transparencyan interference phenomenon, but is it also an interference phenomenon in classical systems?

Electromagnetically induced transparency is a hot topic in physics. However I'm curious about its mechanics in physics. Physicists think that it's a phenomenon of interference from transition of two ...
5
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1answer
125 views

Young Tableaux for $SU(3)$ representations vs. $j=1$ objects

I'm working through Sakurai's Modern Quantum Mechanics and in the section on Permutation Symmetry and Young Tableaux, he mentions that a tableau constructed of $\square = ...
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1answer
39 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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1answer
149 views

Confused by Many-Body Formalism: Creation/Annihilation to Field Operators

I'm going through an introduction to many-body theory and I am getting tripped up on the formalism. I understand quantities such as $\hat {N} = ...
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532 views

Bohr-Sommerfeld quantization from the WKB approximation

How can one prove the Bohr-Sommerfeld quantization formula $$ \oint p~dq ~=~2\pi n \hbar $$ from the WKB ansatz solution $$\Psi(x)~=~e^{iS(x)/ \hbar}$$ for the Schroedinger equation? With $S$ the ...
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3answers
597 views

Does the canonical commutation relation fix the form of the momentum operator?

For one dimensional quantum mechanics $$[\hat{x},\hat{p}]=i\hbar $$ Does this fix univocally the form of the $\hat{p}$ operator? My bet is no because $\hat{p}$ actually depends if we are on ...
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2answers
42 views

Does an excited state wave function depend on state preparation?

Consider a quantum system with a ground state and many excited states (e.g. an atom). If the system is in an excited state, to what extent does its wave function depend on the method of state ...
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1answer
118 views

Stern Gerlach with spin in opposite directions

So for the Stern-Gerlach apparatus, we assume that we either have a particle spin up or spin down. We also have the varying field, $\partial B/\partial z$. This initial configuration results in the ...
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5answers
771 views

What is the entropy of a pure state?

Well, zero of course. Because $S = -\text{tr}(\rho \ln \rho)$ and $\rho$ for a pure state gives zero entropy. But... all quantum states are really pure states right? A mixed state just describes ...
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4answers
288 views

Local EPR-experiments with photons in vacuum?

The principle of non-locality states "that an object is influenced directly only by its immediate surroundings." (Wikipedia) When two entangled particles are measured in an EPR experiment, we ...
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1answer
68 views

Quantum mechanics, operator commutes with Hamiltonian

My textbook said, if an operator $\hat{O}$ commutes with the Hamiltonian, then we can use the eigen vectors of the Hamiltonian as a basis of the Hilbert space, then express the operator $\hat{O}$ in ...
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1answer
221 views

Do particles behave like electromagnetic waves?

From double-slit experiments we know particles have wave-like behavior: they statistically form an interference pattern. My question is: Is this wave-like behavior similar to the photons' behavior? ...
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0answers
50 views

Commutation relation of a operator with Hamiltonian [duplicate]

Given that the eigenvalues of a Hamiltonian operator $H$ are bounded below, will a Hermitian operator $T$ exist such that $[T, H] = i\hbar{\bf 1}$ identity operator?
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9answers
3k views

Is the wave-particle duality a real duality?

I often hear about the wave-particle duality, and how particles exhibit properties of both particles and waves. I most recently heard this in this video. However, I wonder; is this actually a duality? ...
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2answers
103 views

Ground state of Spherical symmetric potential always have $\ell=0$?

I was given a problem where I have a spherically symmetric potential (the exact form is not relevant to this question, I think - but anyway is it 0 for $r\in[a,b]$ and $\infty$ everywhere else) and I ...
6
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2answers
163 views

How can we differentiate between matter and antimatter? [duplicate]

For instance if there was a galaxy, assume it to be made up of antimatter (isolated from other "normal" galaxies), how would we, or rather, would we be able to distinguish if it was made up of matter ...
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0answers
39 views

Wave function of N electrons in a superconductor

Assuming that the wave function consisting of $N$ electrons is $\Psi_{N}(\bf{r_1,r_2,\cdots r_N)}$ then in the presence of a magnetic field ($\bf{B}=\nabla \times A$), how do I show that the current ...
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5answers
255 views

Quantum entanglement and spooky action at a distance

When quantum entanglement is explained in "layman's terms", it seems (to me) that the first premise, that we have to accept on faith, is that a particle doesn't have a certain property (the particle ...
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1answer
48 views

Photon and Wave

There are some aspects of light that can be easily demonstrated by using the concept of wave. However I really want to know what it would be like in term of photon point of view. So I have some ...
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1answer
110 views

Spin Control and Entanglement

I have a thought-experiment sort of question and I don't know where to start. Suppose you have an entangled pair, e1 and e2, and you split them. Then BEFORE reading them, you spin control e1 to +, ...
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1answer
44 views

Koopman Von Neumann state vs Quantum state

Is it correct to think that a state in Hilbert space represents the "most we can know" about a system? Is therefore a state in KvN Hilbert space the same as a state in the usual quantum Hilbert space, ...
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1answer
61 views

Scalable tool (engine) for simulating the universe

Does there exist a large scale scalable tool (engine) for simulating the universe that incorporates both quantum mechanics and cosmology, i.e. micro & macro scales? (It would be best if this tool ...
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2answers
75 views

How can we say that a wave function follows schrodinger equation using operators?

If I have an operator which has an eigenfunction which follows schrödinger's time-dependent equation , and I have another eigenfunction to this operator , can I say that even the other eigenfunction ...
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15 views

Many body quantum rotors

I'm stuck on a particular problem about quantum rotors. Suppose we have $N$ such rotors and they are connected to a thermal reservoir of temperature $T$. Neglecting any center of mass motion, I'm ...
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3answers
143 views

Measurement of quantum state

Consider a particle in a box system.Assume its state to be a superposition of the ground and the first excited energy states.Consider two observers A and B (rest of the world).A made the measurement ...
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2answers
90 views

What is the physical interpretation of a field operator

So far in our lecture we defined creation operators $a^{\dagger}_{n}$ in the following way, that we said: Somebody got you a antisymmetric or symmetric N- particle state and now $a^{\dagger}_{n}$ ...
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1answer
58 views

Energy as charge with respect to time translations in QM

Consider a non relativistic quantum mechanical system with Hamiltonian $\mathcal{H}$, and denote the states by $\psi \equiv \psi(t) \equiv | \psi(t) \rangle$. From the Schrödinger equation we know ...
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2answers
108 views

Why is time evolution of wavefunctions non-trivial?

(Note: This post focuses on a single simple example, however I'm asking about the error in general in my logic). Consider the infinite potential well "particle in a box" system described by ...
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1answer
30 views

How do discretize a finite crystal?

I am trying to find a general method to discretize a finite crystal system. How I have been discretizing systems so far (using Wannier functions): When you have an infinite crystal, you may apply ...
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1answer
72 views

What is the smallest length scale ever measured?

And, by the way, what is, or are, the measured values?
4
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2answers
71 views

How is the scattering length in 2d defined?

Scattering length is 3d is well-defined. In the literature, one can also see scattering length in 2d. How is it defined? Can we even generalize it to 1d?
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2answers
3k views

Can anybody provide a simple example of a quantum computer algorithm?

Does anybody give a good textbook description of a quantum computer algorithm and how its different from an ordinary algorithm?
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0answers
44 views

Phase and group velocity of a soliton? [closed]

How do I find the phase velocity and group velocity of a soliton with a $\operatorname{sech}$ (hyperbolic secant) envelope?
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1answer
46 views

Where did I go wrong in ket vector in quantum mechanics? [closed]

Consider a system of total angular momentum j = 1. The operator jx is given by: What are the possible values when measuring jx? My attempt: The eigenvalues after calculation are -1, 0, 1. Now I ...
2
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1answer
52 views

What is the potential field of an ion near the Bohr radius?

I figure that at large enough distances, the potential field of an ion is just the Coulomb potential for its net charge. But what happens at scales comparable to the ion's Bohr radius? Could there be, ...
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2answers
37 views

Are relative phases observable for identical particles but not for non-identical ones?

In quantum mechanics, amplitudes are represented by complex numbers $e^{i\phi}$, which have phase angles $\phi$. These phase angles are clearly not observable in absolute terms. If I have two ...
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2answers
93 views

Eigenvalues being physical observables

I think I'm comfortable with the PDE solutions to the Schrodinger equation. But as soon as we start putting these values in a matrix (in dirac notation), I lose my understanding and everything ...
2
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3answers
91 views

Fock space and occupation number

I have troubles to understand the concept of a Fock space. We defined it as a direct sum of the 0-particle, single particle, two particle etc. Hilbert space. Unfortunately, I am not sure if I ...
1
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1answer
21 views

Filled molecular orbitals: Avoidance vs Mixing

I am trying to figure out if the mixing of two filled orbitals requires some additional activation energy and, if it does, if there is some orbital avoidance area where the filled orbitals will not ...
2
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2answers
66 views

Why does dot product equal to one? (Pauli spin matrices)

I was reading these lecture notes (NB: PDF): For spin-1/2, the rotation operator $$ R_\alpha^{(s)}(\mathbf n)=\exp\left(-i\frac{\alpha}{2}\vec\sigma\cdot\mathbf{\hat n}\right) $$ can be ...
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0answers
12 views

Crystal in Magnetic Field

When you have a 2D crystal in a uniform perpendicular magnetic field, you can use the Peierls substitution to convert one tight-binding before-magnetic-field-band into a $q$-bands under the influence ...
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0answers
23 views

Hamiltonian symmetry Lie algebra

What is the connection between complete set of commuting observables and generators of the Lie group? I have a Hamiltonian written down in second quantized formalism and I also checked that it ...
0
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4answers
78 views

Complex Conjugate of Wave Function

I've been reading through Griffiths QM book, and the only thing bugging me is they never fully described what $\Psi^* $ should be for any given function. I know it's the complex conjugate at the same ...
3
votes
1answer
169 views

First order coherence through double slit

The state $$|\Psi \rangle = |0\rangle + \sum_j \int d\omega f_j(\omega)\hat{a}^\dagger_j (\omega) |0\rangle $$ is coming from a far field and incident on a double slit setup. Here j is the index of ...
2
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1answer
63 views

Why no Top Physicists Work on Bohmian Mechanics? [duplicate]

I'm curious to hear some opinions from serious physicists on this site as to why no top physicists have ever worked on Bohmian Mechanics. Except Bohm and Bell, the theory has received virtually no ...
14
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5answers
212 views

How is anything *not* ultimately a position measurement?

Consider measuring the momentum of an electron. You pass it through some kind of electromagnetic field, it strikes a photodetector (e.g. a CCD), and you back-calculate out the momentum of the ...
2
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0answers
24 views

What symmetry operation mixes states with different $\ell$ in hydrogen atom? [duplicate]

We can mix states with different $m$ in hydrogen atom by rotating it around some axis (not coinciding with $z$). Thus rotation is the symmetry operation which mixes states with different $m$. As ...
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1answer
49 views

Total magnetic moment in an atom

I have a doubt regarding the calculation of total angular momentum of electron in an atom.Which is the right way to do it? Method 1: Total magnetic moment $$ \begin{align} \vec{\mu_J} &= ...
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2answers
83 views

How to find optical toy models of entangled quantum mechanical systems?

I recently read Arnold Neumaier's lectures on uncovering classical aspects of quantum mechanics: Classical and quantum field aspects of light Optical models for quantum mechanics I can't find the ...