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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delayed choice measurement subsequent analysis

This is a variant associated with the Scully and Druhl signal-idler photon delayed choice experiment, as described and discussed in Brian Greene's Fabric of the Cosmos. The commentary notes the ...
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Is there a quantum mechanical analog to classical rheonomic constraints wherein the Hamiltonian is not the total energy?

The Wikipedia article on the Hamiltonian operator in QM says that the Hamiltonian corresponds to the total energy of the system, but qualifies that statement with a "in most cases" tacked on the end. ...
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If $[A_1, H] =[A_2, H] = 0$ but $[A_1, A_2] \neq 0$, $H$ must be degenerate?

I am having a difficult time understanding this problem. Suppose $[A_1, A_2] \ne 0,$ $[A_1, H] = 0,$ $[A_2, H] = 0.$ Show that the energy eigenstates of $H$ are in general ...
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2answers
46 views

Physical Meaning of Phase Ambiguity

What is the physical significance of multiplying a quantum state $|A>$ by a phase factor $e^{i\theta}$. This does not have any effect on the normalization of the state so what is it physically? ...
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Photons absobtion during quantum jump

According to this article a quantum jump CAUSES photons absoptions. Does it mean that if there is no photon around quantum jump is impossible? https://en.wikipedia.org/wiki/Atomic_electron_transition ...
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3answers
96 views

Is Hamiltonian a differential operator in second quantization?

Normally, a free particle Hamiltonian is written $$ \hat{H} = - \frac{\hbar^2}{2m} \Delta $$ which is a differential operator because Laplacian $\Delta$ is. On the other hand, in second ...
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1answer
22 views

Resistance of a cloud of free electron gas by Kubo formula?

How much is the resistance of a cloud of free electron gas, if at all? How much is the resistance of a cloud of free electrons in a periodic potential? Did anyone calculate it using the Kubo ...
2
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2answers
88 views

Do atoms behave like waves? [duplicate]

I've heard someone state that the double slit experiment can also be done with atoms, not just electrons or photons of light.
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33 views

Approximate Electric Potential $V$ so that it is of the form $V(r) + V(\phi) + V(z)$

I'm trying to simulate the conductivity of a nanowire that is modeled by a cylindrical shell of infinite potential with benzene rings in the core of the wire. (This is based on a coiled-coil protein ...
2
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1answer
48 views

What is the physical significance of Compton wavelength?

Wikipedia says, The Compton wavelength represents the quantum response of mass to local geometry. What does it actually mean?
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2answers
199 views

Electron as a standing wave and its stability

1. When it was an era of classical mechanics we used to believe in the Bohr's atomic model. It interpreted electrons as particles (although I couldn't understand how come Bohr who interpreted ...
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1answer
38 views

Can we extract positrons from gamma rays?

If gamma rays undergo pair production is there a way to say, deflect and collect the positrons using magnetic fields?
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1answer
64 views

Question about Planck's constant

How did Dirac or whoever came up with it know that the momentum operator in quantum mechanics is $-i\hbar\frac{d}{dx}$? How did he know the $\hbar$ was in there? How did all these physicists know ...
2
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1answer
57 views

Basis states for many-particle system

I'm reading these notes about second quantization. In section 1.4 the author introduces many-particle wavefunctions. But I can't understand how basis are defined here. I know that if $\{\chi_i | i=1, ...
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3answers
98 views

Wave Function concept

What do we mean when we say wave function of electron? Does it mean wave nature of electrons? I am really confused.Without clearing this confusion i cannot proceed to molecular orbital theory.I am ...
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1answer
22 views

Semi-infinite / Asymmetric potential well

I'm asked to come up with an ansatz and solve for the coefficients of a asymmetric infinite potential well, where: $$ V = \begin{cases} \infty \text{ for } x< 0 \\ V_0 \text{ for } 0 \leq x \leq L ...
2
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2answers
22 views

What happens to a radioactive element or isotope's electrons when it undergoes alpha decay? [duplicate]

It seems to make sense that when an atom loses two protons, it would lose two electrons as well, but I don't actually know what happens.
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1answer
44 views

Light changes wavelength in the presence of gravity, can the quantum theory of gravity explain this?

If light changes wavelength in the presence of a gravitational field, how can this be described by the quantum theory of gravity?
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1answer
28 views

Circular polarisation destroying interference pattern for double slit

I have been trying to mathematically explain the empirical result that putting orthogonal polarisers (quarter-wave plates) behind the two slits of a double-slit setup will erase the interference ...
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0answers
45 views

Does Only Flat universe have zero energy? [on hold]

Hello I am very new to cosmology and quantum physics. I need some basic understanding (in LAYMANs term )of the following: I read that only closed universe has zero energy. But I heard Astrophysicist ...
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39 views

which of the many interpretations of Quantum Mechanics most well explained? [on hold]

I have been studying the ensemble interpretation by Leslie Ballentine which looks very well explained and has reason for every(almost every) axiom. I am seeking new your opinion.
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26 views

How does Quantum tunneling conserve energy? [duplicate]

How does Quantum tunneling conserve energy? Take a simple example. An electron in hydrogen leaves the single proton it was bound to and escapes without being excited by and interaction. It tunneled ...
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1answer
35 views

Derivation of minimum uncertainty from Squeezed Coherent State [on hold]

I'm studying a book in which I stopped by this point. I don't know how to derive the inequality from $$tr(\rho A^{*}A )?$$
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61 views

Modern Quantum Mechanics, Sakurai [on hold]

As a graduate student am I supposed to finish the entire material of "Modern Quantum Mechanics, Sakurai" ?
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98 views

Can the Born rule be derived? [duplicate]

$\renewcommand{ket}[1]{|#1\rangle}$ If we have a particle and we know the initial state $|\psi\rangle$ of everything that is relevant, and we know the full Hamiltonian $H$, then we should be able to ...
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22 views

How to write electron hole Hamiltonian into quasi-boson form?

V Chernyak, Wei Min Zhang, S Mukamel, J Chem Phys Vol. 109, 9587 (can be freely downloaded here http://mukamel.ps.uci.edu/publications/pdfs/347.pdf ) Eq.(2.2), Eq. (B1) Eq.(B4)-(B6). When I substitue ...
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1answer
87 views

What is the classical counterpart of an eigenstate?

Does this question make sense for every system or just some? If it makes sense, it is a periodic orbit?
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49 views

How does one describe a state with a density matrix after measuring position?

My question is about position measurement in non relativistic quantum mechanics. I've been taught that when you measure the value of an observable for some state of a system described by ...
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1answer
31 views

Convex combinations of states yielding a pure state

Wikipedia states that Geometrically, when the state is not expressible as a convex combination of other states, it is a pure state.[9] The family of mixed states is a convex set and a state ...
1
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1answer
227 views

Total orbital and spin angular momentum for a closed shell

I read one Phys.SE question similar to mine, in Total angular momentum in a full shell but the question was so confusing and vague. The answer, though, was helpful for me to understand a part of my ...
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1answer
36 views

How is work function for a metal in photoelectric effect just one single number?

I mean,there are so many electrons at different positions on the surface of the metal,at different depths with different energies. how is it possible that work function for all the electrons same? is ...
1
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1answer
56 views

Can a photon excite an electron via the uncertainty principle?

An electron is trapped in an infinite well potential with a width of $\Delta x$. A photon of wavelength $\lambda $ < $\Delta x$ is fired at the electron and misses or rather they don't interact. ...
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5answers
802 views

Double-slit experiment: Difference between observing photon path and interference pattern?

This is something that has confused me whenever I read about the double-slit experiment. When the double-slit experiment is performed, I understand that the resulting pattern for the sequentially ...
2
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1answer
47 views

Smoothness of the energy levels of a generic Hamiltonian

Let us take an Hamiltonian $H(\xi)$ which depends on a set of parameters $\xi$, and assume that the matrix elements $h_{ij}(\xi)$ of the Hamiltonian are smooth complex functions of the parameters ...
2
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2answers
120 views

Proof that entanglement is independent of distance

I've already read this quite often but never seen a proof—maybe it's just so clear to physicists, but I'm not really sure how to prove it. Currently I'm pretty confused so the following might be ...
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2answers
32 views

How to express a convex function of a Hermitian operator in terms of its eigenvalues and eigenvectors?

The Hermitian operator $\hat O$ can be expressed as $$\hat{O}=\sum_i O_i|O_i\rangle\langle O_i|.$$ How to prove that a convex function $f(\hat O)$ can be expressed like $$f (\hat O)=\sum_i ...
2
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1answer
388 views

How can it be derived that particles described by the Dirac equation must have spin 1/2?

I am reading some lecture notes that unfortunately don't seem to be available online, but that are quite close in spirit in their treatment of the Dirac equation to Sakurai's "Advanced Quantum ...
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30 views

Corrections in Perturbation theory

Is there a way to construct a bound on the perturbative corrections to a problem in perturbation theory? For example, if I have the standard 1st order correction to the eigensolutions of a problem ...
1
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1answer
47 views

Hermitian conjugate of an antiunitary transformation

In quantum mechanics, one often considers symmetry transformations which are defined in terms of operators which do not change the norm of states in the Hilbert space. For the Wigner's theorem, this ...
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1answer
41 views

Probability Density of a freely falling body

The following question has been taken from David J Griffith's Intro to QM. This is not my homework! :D Suppose I drop a rock off a cliff of height $h$. As it falls, I snap a million photographs, at ...
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15 views

Repulsive component of intermolecular interaction

Intermolecular interaction mainly consists of 2 components: (a) Dipole vs dipole (permanent & induced), which is more likely to be attractive (b) Pauli exclusion, which is always repulsive The ...
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41 views

Are Landau levels always degenerate?

Solving the Landau problem, namely the quantum mechanical problem of a particle in a magnetic field leads to degenerate energy states, the famous Landau levels. My question consists of two parts. ...
3
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1answer
215 views

The dual role of (anti-)Hermitian operators in quantum mechanics

Hermitian (or anti-Hermitian) operators are of central importance in quantum mechanics in at least two different incarnations: Observables are represented by Hermitian operators on the quantum ...
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65 views

How to get Heisenberg Equation of Motion?

If a system Hamiltonian is given by, $$ ...
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1answer
68 views

Dirac Eqn: why separate operators

At some point Dirac writes: (OpA)(OpB)Y = 0 where OpA and OpB are those two brackets that differ only in the sign of m, then he deduces: (OpA)Y = 0 OR (OpB)Y = 0 (or is that AND). I don't get ...
2
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0answers
46 views

Amplitude for a string to propagate from one point to another

In Zwiebach’s book sections 12.6 and 12.7 interesting aspects of the wave function of the string are discussed. In order to introduce my question first recall what happens with the relativistic ...
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Electron wave function seen in Quantum Cascade Laser?

http://sciencequestionswithsurprisinganswers.org/images/qcllevels.gif How did they observe and take a picture of the electron wave function without collapsing it? Does this prove that the wave ...
1
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1answer
42 views

Relativistic probability amplitude of a particle to be in certain position

In the book “The story of spin” by Tomonaga on page 110, it says They insisted that a concept like "the probability of a particle to be at $x$ in space" is meaningless for relativistic ...
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1answer
56 views

How can i only shine/shoot one proton/electron per second? [duplicate]

I would like to test out the two slit experiment but only one electron or proton at a time.
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74 views

Does Digital Physics imply Heisenberg's Uncertainty Principle? [closed]

I made the following observation which led me to believe that perhaps Digital Physics implies Heisenberg's Uncertainty Principle: Consider Noether's Theorem, which states that space-translation ...