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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How does quantum mechanics explain stability of electron orbitals? [duplicate]

According to classical physics, an electron orbiting the nucleus would emit electromagnetic radiation. Losing energy in that way, it would spiral into the nucleus and the atom would collapse. Quantum ...
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39 views

Degeneracy of Rotational Energy Levels of a Diatomic Molecule

To derive the energy levels of a diatomic molecule (with the z axis the axis of symmetry of the molecule), we write the Hamiltonian as ...
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2answers
61 views

What type of Quantum Gate is this

I'm trying to work out if this is a certain type of 'known' Quantum Gate $|1\rangle|1\rangle $ goes to $|1\rangle|1\rangle $ $|1\rangle|0\rangle $ goes to $|1\rangle|0\rangle $ $|0\rangle|1\rangle ...
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46 views

Realism vs. locality in EPR/Bell arena

I understand that this is a much debated issue, so I will try to be precise in order to narrow the question. Bell inequality violation rules out Local Realism. From this, I understand that by giving ...
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36 views

Rotational Spectrum of a Diatomic Molecule

The rotational energy levels of a diatomic molecule are given by $$E_l=\frac{\hbar^2}{2I}l(l+1)$$ where $l$ is an integer. If the molecule is a dipole it can emit or absorb electromagnetic radiation ...
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232 views

Why does replacing bra and ket basis vectors by their row and column representations give the wrong matrix representation in a non-orthogonal basis?

I have a Hermitian operator (for a 2D Hilbert space) given by $$H=|\psi\rangle \langle \psi|+|\phi\rangle \langle \phi|$$ where $|\psi\rangle$ and $|\phi\rangle$ are normalized but not necessarily ...
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1answer
56 views

When is the spectrum of the Hamiltonian (purely) continuous?

Given a quantum hamiltonian $H = \frac{1}{2m}\vec{p}^2 +V(\vec{x})$ in $n$-dimensions, the general rule-of-thumb is that the energy will be discrete for energies $E$ for which $\{ \vec{x} | ...
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2answers
48 views

Angular momentum commutation relations?

Does any operator $\mathbf{T} = (T_1,T_2,T_3)$ that satisfies the commutation relations $[T_i, T_j] = i\hbar\epsilon_{ijk}T_k$ represent an angular momentum operator?
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43 views

Why is the photoelectric absorption coefficient finite at the threshold frequency?

I mean the photoelectric effect of the hydrogen atom. It is weird. By the Fermi golden rule, the transition or absorption rate is proportional to the density of the final states. At threshold, the ...
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1answer
61 views

Meaning of the symmetrisation postulate in absence of a proper model

My question is on the use of the concept of indistinguishable particles (in quantum mechanics) in a very general context and in particular in statistical mechanics. I have made clear some of my ...
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1answer
52 views

Hermitian Adjoint of Spinor

Say we have a four component spinor $\psi$: $$ \psi=\begin{pmatrix}\psi_L\\\psi_R\end{pmatrix} $$ Is the Hermitian adjoint of this: $$ \psi^\dagger =\begin{pmatrix}\psi_L^\dagger ...
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1answer
95 views

Expectation value of Commutator of Hermitian operators [closed]

Assume $\hat{A},\hat{B},\hat{C}$ are Hermitian. $$[\hat{A},\hat{B}]=i\hat{C}$$ and $$\hat{A}|a\rangle=a|a\rangle.$$ Then $$\langle a|i\hat{C}|a\rangle=\langle a|[\hat{A},\hat{B}]|a\rangle =0 .$$ ...
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49 views

Understanding a modified “delayed choice quantum eraser” experiment?

Pardon my ignorance, but I am really interested in understanding the quantum mechanics and it's interesting implications, but clearly I don't, since I keep coming up with violations to many physics ...
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59 views

Why is the electric field operator normalized by a volume?

I came across the following definition of the electric field operator: But I am not sure what this $V$, the "volume of a box", is about. It seems to enter the discussion in order to have standing ...
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1answer
127 views

Has this experiment really demonstrated wave-function collapse?

My question is: why did the following experiment claim that it had demonstrated the wave-function collapse? http://www.nature.com/ncomms/2015/150324/ncomms7665/full/ncomms7665.html I would have no ...
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2answers
88 views

Could quantum particle have a specific velocity without position at all?

I understand that electron spin on different axis is an example of complementary properties, which cannot be measured accurately at the same time. I also understand that if we have an electron is ...
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0answers
21 views

Existance of observables trace orthogonal to Hamiltonian

I need to understand under which conditions there exists an observable (hermitian matrix) which solves $Tr(B \ U(t,s) \ H_c \ U(s,t)) = 0$ for all $s \in [0,t]$ where $t>0$. I am only interested ...
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413 views

Why aren't orbitals symmetric?

In an hydrogen-like atoms the orbitals are solutions to the Schrodinger equation suitable for the problem. They describe the regions where an electron can be found. So, why don't they have spherical ...
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1answer
72 views

Entanglement, Bohr-Einstein Debate, Bell's Inequality

On BBC episode The Secrets of Quantum Physics (Part 1) Jim Al-Khalili explains quantum mechanics for the layman. In the first half, he does a very good job; in the second half, either he thought his ...
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30 views

Mapping quantum states of different (quantum) physical systems to the same Hilbert space [duplicate]

Is it possible to map quantum states of different physical (quantum) systems to the same Hilbert space? For example if I consider two different molecules in the ground state, may I represent them as ...
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22 views

Are atomic energies increasing as the Universe expands? [duplicate]

Starting from the FRW metric (for simplicity flat space, radial direction only): $$ds^2=-c^2dt^2+a(t)^2dr^2$$ If we take $dt=0$ then the proper distance $ds(t)$ between two spatially separated ...
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1answer
135 views

Lorentz Algebra Representation and QFT

I just have a trouble making a full analogy between Lorentz Algebra Representation in Quantum Field Theory (QFT) and SU(2) representation in Quantum Mechanics (QM). To make my point, I will write few ...
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1answer
37 views

Continuity behaviour of a wavefunction when the potential exhibits a discontinuity

If a potential $V(x,t)$ exhibits a finite discontinuity in space, the wavefucntion $\phi(x,t)$ and its spatial derivative will be continuous. If a potential exhibits a finite discontinuity in time, ...
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5answers
99 views

The nature of measurement

Does the measurement of the particle change it's physical state? Or does it only seem to do that? Ex. if a particle was measured before the slits, would we see an interference pattern, or a particle ...
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1answer
52 views

2s orbital wavefunction has non-zero probability at $r=0$? [duplicate]

The wavefunction for an electron within a hydrogen atom in the $2s$ state has the following wavefunction: ...
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46 views

potential barrier scattering when particle energy equals to the barrier height

What happens if we have $E=V$, where $E$ is the energy of a incoming particle and $V$ is the height of a square potential barrier? This wiki page actually gives a finite transmission probability for ...
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2answers
77 views

Selection rule $\Delta S=0$: Why does a photon not interact with an electrons spin?

When talking about selection rules in atomic physics, many books state that the photon interacts with the electrons angular momentum such that that $\Delta l=\pm 1$. Absorbed/emitted photons exchange ...
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1answer
52 views

What is the difference between the photoelectric effect and secondary emission?

What is the difference between photoelectric effect and secondary emission in photo multiplier tubes? In other words, why the difference between the energy of the incident photon and the work function ...
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2answers
61 views

Particle in a one dimensional box conditions

Why does the wave function have to be $C^1(\mathbb{R})$ for a finite square well but not for an infinite square well? For an infinite square well with boundaries at $x=0$ and $x=L$, we have ...
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1answer
185 views

How to find 2nd order pertubation to wave function? [closed]

Today, I'm looking for how to find the 2nd perturbation to the wave function in Rayleigh Schrödinger Perturbation Theory (RSPT). SETUP Starting from the 2nd order perturbation in Dirac's notation: ...
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1answer
67 views

Why do electrons in a superconductor lack energy to produce “massive” photons

My two questions are based around looking for a good, simple (if possible) explanation of the Cooper pair effect in superconductors. I follow the idea that, in intuitive terms, "a Cooper Pair" ...
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40 views

How can I create particle-in-a-box diagrams in LaTeX? [migrated]

Interested in creating particle in box diagrams at various energy levels and dimensions. Does anyone have source code to do so or suggestions of good packages to use?
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3answers
123 views

Why does the density matrix $\rho$ obey a wrong-signed Heisenberg equation of motion?

The density matrix is defined as $$ \rho_\psi ~:=~ \frac{\lvert\psi(t)\rangle \langle \psi(t)\vert}{ \langle \psi(t) |\psi(t)\rangle }$$ in the Schrödinger picture. $\rho_\psi$ is obviously a time ...
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40 views

Ballentine's proof of (one half of) Stone's theorem

Reading Ballentine's "Quantum Mechanics; A Modern Development" I got stuck on his really short proof of what I think is Stone's theorem. On page 65 (paperback, reprint of 2008) he writes about about a ...
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2answers
74 views

Blackbody radiation and emissive power

According to blackbody radiation theory, and thanks to Planck, we now know that there is a energy density, $u(\lambda,T)$ [$J/m^3$], associated with a certain wavelength at a particular temperature. ...
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1answer
46 views

Finding finite square well width and depth from transmission resonance

For an electron incident a one-dimensional finite square well the transmission probability is $\approx$1 for electron energies $E_1=0.6 \textbf{ eV}$, $E_2=1.9 \textbf{ eV}$ and $E_3=3.4 \textbf{ ...
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1answer
62 views

Probability of photon emission

If a photon of a given wavelength is absorbed by an electron (for simplicity, let's assume the electron has only one excited state), does the probability that the electron jumps to its excited state ...
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2answers
74 views

Combinations of angular momentum

The following diagram is taken from this Wikipedia page: It illustrates how we may only know the total orbital angular momentum $L$ (so the radius on our sphere in $L$ space) and the z-component of ...
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2answers
56 views

How does the time evolution of a hydrogen atom work?

If I am given the initial stationary spatial wavefunction of a hydrogen atom, how does it change through time? I'm wondering if it is the same as the time evolution of any old stationary state, that ...
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2answers
50 views

$p^4$ in radial coordinates not Hermitian

Griffiths' quantum textbook claims in question 6.15 that "$p^2$ is Hermitian, but $p^4$ is not, for hydrogen states with $l=0$." First off, I am puzzled at his use of terminology. An operator is ...
2
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1answer
136 views

Is entanglement a classical phenomena?

If I have an entangled state shared between two parties Alice and Bob $$\frac{1}{\sqrt{2}}|00\rangle+\frac{1}{\sqrt{2}}|11\rangle....(1)$$ then the reduced density operator of Alice's side is ...
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44 views

Calculating an integral containing a commutator for the hamiltonian and spin for a one electron atom

Problem: Calculate the following integral for a 1-electron atom $ < 2 p_x\alpha \,\, |\,\, [\hat{H},\hat{S_z}] \,\,|\,\, 2 p_x\alpha > $ This is my attempt at a solution: $$ \, ...
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1answer
63 views

Translation Operators

Show that if the wave function $\langle x|\psi\rangle$ is modified by a position-dependent phase $\langle x|\psi\rangle \to e^{\frac{ip_ox}{\hbar}}\langle x|\psi\rangle$ then $\langle x\rangle ...
3
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1answer
91 views

What's the significance of the difference between the quantum numbers, $\ell$ and $m_{\ell}$?

I know that $m_{\ell}$ is associated with the projection of the angular momentum vector onto the $z$ axis and $\ell$ is associated with the length of the angular momentum vector. To me this implies ...
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1answer
68 views

Quantum Entanglement

My book is generally being quite unclear about something. So firstly I know that if the system is not entangled, we can write its state as $|ab\rangle=|a\rangle|b\rangle$ (if we understand the ...
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27 views

Unitary base transformation applied to continous bases

For discrete vector spaces one can define a unitary base transformation between two complete orthogonal bases $\{ | b_k \rangle \}$ and $ \{ | a_k \rangle \}$ as $$U = \sum \limits_k | b_k \rangle ...
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1answer
76 views

Proper way to quantize the string in the light-cone gauge

In many books like Polchinski and Green-Schwarz-Witten the light cone quantization is carried out in a fast way. They just use the virasoro constraint in the light-cone gauge to get the ligh-cone ...
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1answer
52 views

Commuting with time evolution operator implies commuting with Hamiltonian

Consider a quantum system (finite dimensional) has overall Hamiltonian: $H_t = H_0 + w(t)H_c$ with $H_0, H_c$ constant in time and traceless and $w(t)$ a, not too badly behaved, function of time. ...
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1answer
37 views

Translation Operator

Let $|\psi\rangle \to |\psi'\rangle = \hat{T}(\delta x)|\psi\rangle$ for infinitesimal $\delta x.$ Show that $\langle x \rangle' = \langle x \rangle + \delta x$ and $\langle p_x \rangle' = \langle ...
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1answer
70 views

Considering spin angular momentum, what is the magnetic moment of a hydrogen 1s electron, and its energy levels?

This question, posed in a problem sheet that I have been asked to do, has stumped me. I really don't know what to do here. Any help would be greatly appreciated. I know that the magnetic moment of an ...