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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The uncertainty principle and spin

I realize that this may be a very basic question, but I've been unable to find the answer elsewhere so thanks in advance for the help. Suppose an electron's spin is measured about an axis, and then ...
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51 views

Quantum Physics..so what do you think? [duplicate]

We have de Broglie's equation for the wavelength of matter waves.well...we know that we neglect it in classical mechanics.Consider a space rocket or something that 's moving really fast.In a space ...
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33 views

How can a spinor represent an “epistemic” state?

I have read a lot of stuff on the seemingly endless debate on ontology/epistemology of the quantum state $\psi$. But I always wonder: how can a spinor be considered epistemic when $\psi$ really ...
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14 views

Explanation for orientation entanglement

I have to write a summary for "orientation-entanglement": the state of an object/subsystem depends in general not only (locally) on its configuration in space, but also (nonlocally) on its topological ...
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3answers
159 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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1answer
203 views

Why is the orbital angular momentum of a pi electron along the axis of two atoms' molecule one?

I'm reading quantum chemistry. The book says that the orbital angular momentum of a $\pi$ electron along the symmetry axis of a molecule made up of two atoms is $\pm 1$. I think this is a primary ...
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2answers
166 views

Understanding basic quantum mechanics notation

I was talking with a guy about energy levels of an atom in a magnetic field. He said that energy levels are shifted and that, if you want know how much, you have to analyze this: for 1s state: ...
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1answer
63 views

What do atoms really look like?

When considering the orbital model of the atom it seems like the shape of each orbital corresponds the shape that contains a volume such that there is a 90% chance of an electron being there. I also ...
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0answers
20 views

Measuring the coherence between degenerate atomic ground states [closed]

Given a 2-level atom with the degenerate ground state and excited state with $j_g =j_e =1/2$. Assume that initially the atom is prepared in pure state with all the population in its ground state. What ...
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1answer
134 views

Correct way to do a Thomas-Fermi approximation for cold gases

I have calculated the total Gross-Pitaevskii energy for a 2D Bose-Einstein condensate in an harmonical trap, using a variational gaussian wave function with a variational parameter b. Now I want to ...
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1answer
29 views

Is there an equivalent probability distribution for fermions and bosons to the expression for distinguishable particles

So the particle distribution of two particles is simply $$ P_{12}=P_1(r_1)P_2(r_2) $$ where $ P_{12}$ is simply the modulus of the total wavefunction squared and $ P_1 $ and $ P_2$ are the the ...
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4answers
275 views

Does $\lvert\langle p\lvert\psi\rangle\rvert^2$ have any meaning at all?

I used to think $\lvert\langle p\lvert\psi\rangle\rvert^2$ had the meaning of some likelihood of the particle's momentum being $p$ (within some tolerance interval $\Delta p$). Now I'm just confused. ...
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2answers
769 views

Coupled quantum harmonic oscillator

Given the following Hamiltonian for two identical linear oscillators with spring constant $k$ and interaction potential $\alpha x_1x_2$; I was asked to find the expectation value $\langle ...
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2answers
71 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, ...
3
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1answer
182 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 ...
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34 views

Are there resources for simulating and/or theoretically describing solitons?

Recently there are striking new ideas emerging on "lower level" dynamics with respect to quantum mechanics involving fluid mechanics principles, including hints of soliton-like aspects to particle ...
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1answer
84 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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1answer
53 views

Are all properties entangled when one property is entangled?

When one or more particles are quantum entangled by say their spin property, do their other measurable properties (e.g., momentum, polarization, whatever?) become entangled as well?
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33 views

Variational principle proof (summing over $n$)

From http://en.wikipedia.org/wiki/Variational_method_%28quantum_mechanics%29 $$= \sum_n \sum_m c_n^*c_mE_m \langle \psi_n|\psi_m \rangle$$ $$= \sum_n |c_n|^2E_n$$ I just want to better understand ...
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1answer
99 views

Quantum simple harmonic oscillator interpretation

I am just wondering what does the SHO system from quantum mechanics actually physically represent? Is it just a SHO of a quantum particle, seems a little too obvious for quantum theory? I'm from a ...
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1answer
81 views

What exactly happens at the second-order phase transition of the 2D Toric code?

For a 2D Toric code specified by $$H = -J_s\sum_{s} \prod_{j\in s} \sigma^x_j - J_p\sum_{p} \prod_{j\in p} \sigma^z_p - h_x\sum_{l} \sigma^x_l - h_z\sum_{l} \sigma^z_l$$ where $s$ denotes stars, $p$ ...
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26 views

Wigner $d$-matrix for $j=1$

In Sakurai's Modern Quantum Mechanics p.198-199, he states that for the matrix $$J_y^{(j=1)} = \frac{J_+-J_-}{2i} = \frac{\hbar}{2} \begin{pmatrix} 0 & -\sqrt{2}i & 0 \\ \sqrt{2}i & 0 ...
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1answer
171 views

Is WKB really applicable for the ground state?

It seems that WKB is applicable for a given $E$ if and only if $\hbar$ is sufficiently small. Or in other words, WKB is applicable if and only if the quantum number is large enough. Is this ...
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2answers
300 views

Can expectation value be imaginary?

I was solving a problem and the result of the expectation value of an operator came out to be $-\frac{\hbar}{4}$ $i$. Is this result possible? It seems counter intuitive.
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4answers
990 views

Which Schrödinger equation is correct?

In the coordinate representation, in 1D, the wave function depends on space and time, $\Psi(x,t)$, accordingly the time dependent Schrödinger equation is $$H\Psi(x,t) = ...
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2answers
114 views

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

If I have an operator which has an eigenfunction which satisfies Schrödinger's time-dependent equation, and I have another eigenfunction of this operator, can I say that the other eigenfunction will ...
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2answers
186 views

Can the momentum eigenstates be non-orthogonal?

Consider the Hilbert space of a particle, whose position domain is confined to $q\in[0,1]$ (e.g. a particle in a box with unit width). Using $$ 1=\int_0 ^1 dq |q\rangle\langle q| $$ and the position ...
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0answers
27 views

How to derive the electron dipole selection rule in coupled bases?

We need to find $| \psi_f \rangle$ fulfilling the condition that $$ | \langle \psi_f | \mathbf{x} | \psi_i \rangle |^2 \neq 0.$$ When using the uncoupled bases $| l,m,m_s \rangle$ I can derive the ...
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2answers
71 views

Calulate the eigenvalues and the possible states after measurement [on hold]

An observable is given by $$\sum\limits_{n= 1}^N a_n|a_n\rangle\langle a_n | $$ Here $\langle a_n |a_m\rangle = \delta_{nm}$. What are the possible measurement results corresponding to the operator ...
6
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1answer
80 views

Why does this condition ensure that the residue of the propagator is 1?

The corrected propagator is given by $$\Delta'(q)=\frac{1}{q^2+m^2-\Pi^*(q^2)-i\epsilon}$$ ($\Pi^*$ is the sum of all irreducible one-particle amplitudes) I get that the residue of the original ...
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0answers
16 views

Energy conservation if photon absorbed below resonance

Suppose I have some quantum system (like atom) with excitation energy $E_{exc}$ which is homogeneously broadened due to finite lifetime. I shine light with narrow spectrum centred around energy ...
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2answers
43 views

What kind of potentials can be used in Schrödinger's equation?

I have a couple of questions about what kind of potentials can be used in Schrödinger's equation: How about the potential from a magnetic field? Isn't Dirac's equation more appropriate in that case, ...
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33 views

Asymptotic Analysis of 1-D Schrödinger Equation [closed]

I'm looking to do a small personal project regarding the time independent Schrödinger equation in 1-D: $$y'' +V(x)y=Ey$$ $$y''=Q(x)y$$ where $ Q(x):=E-V(x) $. There is obviously nothing stopping ...
3
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1answer
157 views

About the nonlocality of QM and faster-than-light/backward-in-time machines

The fact the quantum mechanics is nonlocal is known already for a long time, since the Bell works (1966 and later) and the Aspect's group experiments confirming the Bell-type CHSH inequality (1980 ...
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19 views

Selection rules for iodine

I try to find some selections rules for the electrionic transitions. I know the Wigner Eckart theorem an the dipole approximation. With that it's easy to find some selections rules for hydrogen. But ...
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0answers
59 views

About long range entanglement [closed]

“topologically non-trivial” ground states have long-range entanglement. Is this possible to process the quantum information with help of the studies in topological non-trivial ground states for ...
2
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2answers
123 views

Does Bell's theorem sort out local field theories?

For example the Maxwell's equations is a local theory. It's a set of differential equations that describe how should the state at a point change based on its neighbourhood. Counter example: Newtonian ...
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1answer
56 views

Bell's original inequality in "Speakable and Unspeakable in Quantum Mechanics

I'm having difficulty in understanding the setting for the derivation of Bell's inequality. The passage which sets the context below is from the beginning of the second essay in "Speakable and ...
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2answers
65 views

Can someone clarify which (if any) of these three QM assumptions is wrong?

I am trying to learn more about quantum mechanics. I am reading a book by Griffiths that I like. I'm trying to summarize what I've learned. So below I provided three assumptions. I'd like to know if ...
2
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1answer
80 views

Is the Hilbert space spanned by both bound and continuous hydrogen atom eigenfunctions?

As e.g. Griffiths says (p. 103, Introduction to Quantum Mechanics, 2nd ed.), if a spectrum of a linear operator is continuous, the eigenfunctions are not normalizable, therefore it has no ...
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1answer
75 views

relation between photon number and energy

Suppose there are two light beams. One is red while the other is violet. The energy of both is the same. Which one of these beams has a larger number of photons, or is the number of photons relevant? ...
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1answer
41 views

Variational Principle to find Energy Eigenfunctions

In Quantum Mechanics one can estimate an upper bound for the ground state energy with the following functional: $$\mathcal{F}[\psi(x)] \equiv \int_{-\infty}^\infty \psi^*(x)\hat{H}\psi(x) \,\, dx ...
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normal degeneracy and the “span” of an irreducible representation

In Tinkham's "Group Theory and Quantum Mechanics", Tinkham defines normal degeneracy so that the span of the action of the Hamiltonian's symmetry group on any energy eigenstate yields all possible ...
3
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1answer
499 views

At what angle does a single atom “reflect” a single photon?

Does this question make sense in the quantum world? Imagining a single photon (wave packet?) interacting with a single atom (its electrons etc) how do we currently describe/define the emitted photon ...
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1answer
38 views

Cayley's expansion

Is Cayley's expansion $$\exp(-iH\delta t) \psi(x,t)=\frac{1-\frac{i\delta t}{2}H}{1+\frac{i\delta t}{2}H}\psi(x,t)$$ valid for any operator $H$? What conditions should $H$ fulfill?
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100 views

QM rotation operator

I have seen the proof that for fermions a rotation of $2 \pi$ does not return a spin angular momentum eigenstate to its original form, but instead multiplies the wavefunction by $-1$. Here is an ...
2
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1answer
2k views

How to find the wavefunction that solves an infinite square well with a delta function well in the middle?

Solutions for the wavefunction in an infinite square well with a delta function barrier in the middle are easily found online (see here for an example). I am wondering what the wavefunction is for an ...
2
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2answers
88 views

What Planck units are limits?

Some Planck units, like time, length, or temperature, describe a physical maximum or minimum, at least approximately: you can't get hotter than the Planck temperature, measure anything smaller than ...
2
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1answer
216 views

What can tunnel through a graphene sheet?

In popularizations, people tunnel through walls or doors. But what can really tunnel through a graphene sheet without tearing it? According to Wikipedia, a single layer of graphene absorbs 2.3 % ...
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124 views

Fock Space and fermionic annihilation & creation operators

I have been trying very hard to understand, I am reading Ballentine's book on this topic, but I need help: I realized that I don't understand how many particle states work with the creation & ...