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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Path dependent phase in quantum mechanics

In elementary treatments of quantum mechanics, we are taught that the wavefunction of a single particle is complex valued ($\Psi : \mathbb{R}^3 \to \mathbb{C}$). In particular, the wavefunction has a ...
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5 views

Metastable bound state in resonance scattering

In resonance scattering, why does the mean lifetime of the "metastable" bound state depend inversely on the width of the resonance?
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2answers
34 views

Spin State Energy Levels

When a spin-1/2 particle is placed in a magnetic field that is strong enough and varies slowly enough in space and time, it will become polarized and its spin will either align or anti-align with the ...
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2answers
76 views

“Equidistant” spectra in quantum mechanics [duplicate]

In one-dimensional quantum mechanics, it seems that the only kind of potential able to produce an "equidistant" spectrum, i.e. with $E_{n+1}-E_{n}=\text{constant}$, is the harmonic oscillator. Why is ...
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2answers
91 views

Why superpositions? [on hold]

I've seen a lot of stuff on superpositions, namely the double slit experiment. And every video I watch, it tells me the same thing: It's amazing that when these particles are being observed they ...
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2answers
24 views

How can I calculate the partial trace for a combined state of a pair of two-level atoms to get a reduced state?

Let's say I have a combined state of a pair of two-level atoms, $A$ and $B$, given by the density matrix: $$ \rho = \frac{1}{2}\mid g_A, g_B \rangle \langle g_A, g_B\mid + \frac{1}{2} \mid g_A, e_B ...
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31 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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15 views

What is the connection between Bragg's condition with reduced EK diagram?

In my course notes the professor mentioned that there was some relationship between the Bragg's condition and the first Bernoulli zone of the reduced EK diagram. Specifically, the boundary before ...
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3answers
62 views

Levi-Civita symbol and Hermitian conjugate

When we take the Hermitian conjugate/dagger of an operator expression which contains a Levi-Civita symbol, do we need to transpose the Levi-Civita symbol? E.g., for the crossproduct ...
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1answer
101 views

Questions about the formalism of Quantum Mechanics

I have to do a presentation on this. I'm not expected to do something really detailed, but I'm not understanding the mathematical formalism. I would like to receive general answers to these questions: ...
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64 views

Quantum Mechanics and Economics… What

I was reading this paper: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2002698&download=yes The author has the model presented here: ...
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2answers
76 views

What state does the particle in a box occupy?

My textbook derives the equations for the different energy states $E_n$ of the particle in a box. But my professor in class said this example was a good one because it spoke about the "superposition ...
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3answers
134 views

What is the meaning of “ Ψ is not a measurable quantity in itself”?

I want to know that why the wavefunction Ψ as a complex quantity (i.e $A+iB$ form) in quantum mechanics and somewhere I have studied that Ψ is not a measurable quantity in itself that's why we ...
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1answer
34 views

About shift operators

The question is this: Does $$L_+ L_- Y_{lm} $$ ,where $Y_{lm}$ is a spherical harmonic function, equals to zero. If so, why? The two operators above are defined as $$L_+ ={L_x + iL_y } $$ $$L_-={L_x ...
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1answer
58 views

Considering $\langle \underline{q} \mid \underline{p} \rangle=\frac{1}{(2\pi\hbar)^{n/2}}e^{i\underline{q}\cdot\underline{p}/\hbar}$ [duplicate]

I have been given the following complete systems of eigenvectors $$\mathbf{Q}\mid\mathbf{q} \rangle=\mathbf{q}\mid\mathbf{q} \rangle, \quad \mathbf{P}\mid\mathbf{p} \rangle=\mathbf{p}\mid\mathbf{p} ...
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51 views

Deriving effective model without integrating out degrees of freedom in path integral formalism?

In path integral formalism of quantum field theory (particle physics or condensed matter), one can in principle integrate out part of the degrees of freedom so as to attain an effective model ...
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35 views

what is a clock state?

What is a clock state in atomic physics ? I read this term here http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2708678/ and tried to find a reference to explain the same but have been unable to find this ...
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30 views

Angular momentum wavefunctions with respect to different axes

I've been learning about quantum angular momentum, and I have a question about the relationship between quantum mechanical angular momentum wavefunctions with respect to different axes. I know that ...
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1answer
20 views

Can a particle accelerator really be constructed which can actually change the properties of a material (create a new kind of atom)? [on hold]

Can a particle accelerator really be constructed which can actually change the properties of a material (create a new kind of atom)? If not, what are some ways to create or synthesize a new atomic ...
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1answer
98 views

What happens in a universe with only two electrons? [on hold]

What happens in a universe with only two electrons? Do they stay as waves or do they collapse into particles?
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15 views

For an entangled state consisting of systems A and B, if A is measured when does the wavefunction at B collapse? [duplicate]

If there are two systems A and B, with an entangled state consisting of $$\mid \psi \rangle = \frac{1}{\sqrt{2}} (\mid \uparrow _A \rangle \,\, \otimes \mid \uparrow _{B} \rangle \,+ \mid \downarrow ...
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1answer
87 views

Commutator and Hamiltonian [on hold]

Assume that $[\hat{A},\hat{H}]_-=0$ and $[\hat{B},\hat{H}]_-=0$ but we know that $[\hat{A},\hat{B}]_-\neq 0$. Then there exists degenerate stationary states of $H$. How to prove it?
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2answers
51 views

Derivation of plane wave from inner product of position ket and momentum ket

In textbooks it seems to be taken for granted that $$\langle \mathbf{r}|\mathbf{k}\rangle ~=~ \frac{1}{\sqrt{\Omega}}\exp(i\mathbf{k}\cdot\mathbf{r}).$$ I'm sure it's obvious but is there a ...
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2answers
45 views

Understanding notation regarding particles states and wavefunctions

In the development in my notes of second quantisation I have a problem in understanding notation. We start by considering a basis $\psi_i(\mathbf{r})$ for the Hilbert space of single particle ...
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1answer
59 views

Quantum mechanics and Classical limit(s)

I have tried to make sense of this and i am not sure i get it. What i gather from this page about the classical limit is: You need coherent states something like $\hbar \to 0$ is not really enaugh. ...
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3answers
86 views

Physical meaning of quantum interpretations [on hold]

Do interpretations of quantum mechanics have physical meaning? An argument for no would be the fact that no matter the interpretation, one gets the same measurements. They also do not follow logical ...
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1answer
62 views

Can reduced density matrices of sub systems of an entangled composite system be different?

In a 4-dimensional hilbert space, only 4 entangled states( normalized ) are possible ( if I am not wrong ), the bell basis. In each of the state in bell basis the reduced density matrix is ...
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45 views

Is there a physical interpretation of Neumann boundary conditions for the free Schrodinger equation on a domain?

Let $\Omega$ be a domain in $\mathbb{R}^n$. Consider the time-independent free Schrodinger equation $\Delta \psi = E\psi$. Solutions subject to Dirichlet boundary conditions can be physically ...
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1answer
56 views

Can I say that physical entities do not exist and everything is observed “as if” they exist? [on hold]

Maybe it is a bit philosophical question. If I have a model of the universe with all the laws in a computer program. Can I say that the electrons that are modelled in the program exist ? For me it is ...
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1answer
20 views

Monoatomic fluids and free space around atoms

In monoatomic fluids the atoms can move quite freely around each other. Is there any thermodynamic/statistical mechanic equation how much free space there is between the atoms? This has to be ...
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12 views

Classical limit and generalized coherent states

In quantum optics coherent states introduced by Glauber have a localized probability distribution in classical phase-space with maximum following classical equations of motions. This is not a ...
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Measurement of two qubits in a tensor product space

I understand that if we have two qubits, say $\Psi \in \mathcal{H}_1 \bigotimes \mathcal{H}_2$ where Alice has the first qubit, and she makes a measurement and ends up with the state $\phi \in ...
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Physical significance of Cayley Transform

In the book on Quantum Mechanics by Capri (in Chapter 6), its said that an operator $A$ is self adjoint if the operator, $U$ given by $$ U = (A - i I)(A + i I)^{-1} = -(I+iA)(I-iA)^{-1} = -\text ...
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24 views

Time dependent and Time Independent Schrödinger Equation [on hold]

What is the meaning of Schrödinger's Time dependent and Time Independent Equation?
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3answers
222 views

Normalization problem with hydrogen wavefunction

Suppose you have a mix of states made up of the Hydrogen $\lvert nlm \rangle$ states where one of the coefficients is unknown. For example: $$ \lvert \psi\rangle=A\lvert 100\rangle + ...
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19 views

Unitarity of Symmetrisation operators

How can i proove that the symmetrisation operators $S_{\pm}$ are unitary? Defining $S_{\pm}$ on the $N$ Particle Fock Space by it's effect on $|\Psi \rangle=| \Psi_1 \rangle \otimes... \otimes| ...
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27 views

Is my window's semi-transparency a consequence of elementary quantum mechanics? [duplicate]

Studying mathematical concepts of quantum mechanics, I have recently become familiar with the classical model of one-dimensional particle being scattered by a potential barrier. As a mathematician, I ...
3
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2answers
59 views

Why do we not require higher derivatives to match at boundary when solving the Schrödinger equation in a given potential?

When solving the time independent Schrödinger equation for a given potential in 1D, the main part of the solving involves matching boundary conditions. Usually, we require the value and the first ...
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1answer
33 views

Question regarding NaCl equilibrium separation

So I am tutoring someone later and one of the problems is from Eisberg/Resnick Ch 12. The potential energy $V$ of NaCl can be described emperically by $$V = \frac{-e^2}{4\pi\epsilon_0 ...
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13 views

what does the i-v curve in josephson junction mean?

according to the i-v curve for Josephson junction tunneling for S-I-S (superconductor-insulator-superconductor): do we have any tunneling current for 0< V<= Vc ? if yes, then why don't we show ...
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29 views

Rotation of a spin polarization meaning

I've got some quantum state $|s\rangle =\left( \begin{array}{c} cos(\frac {\theta}{2})\\ {e}^{i\phi}sin(\frac {\theta}{2})\end{array} \right)$ I operate on it with a Paul matrix $\sigma_z$ and get a ...
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0answers
41 views

What is the relation between phase space formulation with Wigner quasi-probability distributions and path integral formulation of quantum mechanics?

I am trying to conceptually connect the two formulations of quantum mechanics. The phase space formulation deals with Wigner quasi-probability distributions on the phase space and the path integral ...
5
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38 views

Why do flux qubits have to be micrometer-sized?

Flux qubits are made using micrometer sized Josephson junctions. They exploit superconducting properties to create and interfere with the magnetic flux between them. My question is that I've seen ...
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30 views

Shor's quantum error correction code with unknown basis

$\newcommand{\ket}[1]{\lvert #1 \rangle}$I've met a problem in quantum secret sharing which involves the use of a quantum error-correction code. (let's make it simple to be the 9-qubit Shor code) In ...
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20 views

Why must the Gamow state be exponentially increasing?

Why must the Gamow state be exponentially increasing? Why cannot it be exponentially decreasing? The energy is $E- i \Gamma$, but the square root of $E- i \Gamma $ can have either positive or negative ...
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1answer
67 views

Why is probabilty conserved under time evolution of a system in quantum mechanics?

I've studied quantum mechanics to a certain degree, but one question that I've never been able to get a fully satisfactory answer to is why probability is conserved (by this I mean that it has either ...
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Quantum mechanics question in derivation of Heisenberg-Euler Lagrangian in Schwartz “QFT” notes

In http://isites.harvard.edu/fs/docs/icb.topic1246957.files/IV-9-EffectiveActions.pdf (Page 20) Schwartz derives the Heisenberg-Euler Lagrangian using Schwinger's proper time method. To do so, he ...
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1answer
38 views

Why is this spin expectation value a vector

I'm given a spin state: $|s\rangle$ = some linear combination of $|\uparrow\rangle + |\downarrow\rangle$ possibly with an imaginary component. $\hat{\mu}_e = g\mu_B\hat{\sigma}$ $g$ is the ...
2
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3answers
61 views

How do I operate on a spin state with a sigma operator?

For any arbitrary spin state $|s\rangle$. How do I operate on it with the Pauli spin matrix, $\hat{\sigma_z}$? Does this have something to do with a Bloch sphere?