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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Calculating Ground State Energy in 1D Potential

Given potential $V(x) = Asec(x)$ for $x > 0$. I want to calculate the ground-state energy $E_0$ via the Schrödinger equation. I'm completely stuck on this one. I've set up the time-independent ...
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2answers
389 views

Transition between 2D and 3D quantum systems

Quantum Hall effect and anyonic particles are examples that occur in a two-dimensional system. However, experiments for such systems can only be realized in a pseudo-2D environment, where the third ...
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1answer
2k views

How exactly is the propagator a Green's function for the Schrodinger equation

Sakurai mentions that the propagator is a Green's function for the Schrodinger equation because it solves $$\left(H-i\hbar\frac{\partial}{\partial t}\right)K(x,t,x_0,t_0) = ...
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4answers
2k views

Are quantum mechanics calculations useful for engineering?

I heard it's is pretty tough to get results for more than a few quantum particles. Are quantum mechanical calculations useful at all for any technology that is being sold? Or do they use ...
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1answer
308 views

A question about definition of Fermi energy

Wikipedia states the definition of Fermi energy as for "a system of non-interacting fermions". If we have to assume free electrons in a solid behave this way before we are able to calculate Fermi ...
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4answers
603 views

Why is quantum physics needed to explain photosynthesis?

Why is quantum physics needed to explain photosynthesis? In what aspect does the corresponding classical theories for photosynthesis fail?
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306 views

What really is the future about the Standard Model

The fact that the bosons of the weak force have mass is something that I think technically poses many problems. To avoid this and other problems with the masses of the particles devised a mechanism ...
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1answer
386 views

Multiplication of 3-vector operators

I've started reading "Quantum Mechanics: A Modern Development" by Leslie E. Ballentine and have some trouble understanding how to handle 3-vector operators (i.e. an operator $\mathbf{A}$ with ...
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1answer
178 views

Event-by-Event Simulation of Quantum Phenomena

I just recently stumbled over http://rugth30.phys.rug.nl/dlm/ and http://www.sbfisica.org.br/bjp/files/v38_26.pdf As the title suggests these are presentations of mathematical models capable of ...
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4answers
446 views

Is the quantization of the harmonic oscillator unique?

To put it a little better: Is there more than one quantum system, which ends up in the classical harmonic oscillator in the classial limit? I'm specifically, but not only, interested in an ...
5
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1answer
390 views

The quantum-mechanical description of an electron motion in a magnetic monopole field

The quantum-mechanical motion problem of an electron in electric field of the nucleus is well known. The quantum-mechanical description of electron motion in a magnetic field is also not difficult, ...
3
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1answer
194 views

Virtual particles in semiclassical Quantum mechanics

(I'm just wondering if some of the concepts in QFT can be exported back to QM, especially the concept of virtual particle) So I've just read Arnold Neumaier's description about virtual particle in ...
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2answers
633 views

Implementing simple atom model using density functional theory (DFT)

I am trying to write computer code which will find the energy and density function for an atom with $Z$ protons and $N$ electrons. I am working in 1D for simplicity and would like to make the overall ...
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1answer
189 views

What does the appearance of a classical particle fundamentally reduce to?

I've been reading an article that describes what seems to be a classical particle as a regularity in the global wavefunction over a quantum configuration space: When you actually see an electron ...
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3answers
2k views

A book on quantum mechanics supported by the high-level mathematics

I'm interested in quantum mechanics book that uses high level mathematics (not only the usual functional analysis and the theory of generalised functions but the theory of pseudodifferential operators ...
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6answers
165 views

Multiqubit state tomography by performing measurement in the same basis

For a $n$-qubit state $\rho$ we perform all projective measurement consisting of one-particle measurements in the same basis, that is, $$p_{i_1i_2\ldots i_n}(\theta,\varphi) = \text{Tr}\left \{ \rho ...
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1answer
162 views

Monte Carlo integration over space of quantum states

I am currently facing the problem of calculating integrals that take the general form $\int_{R} P(\sigma)d\sigma$ where $P(\sigma)$ is a probability density over the space of mixed quantum states, ...
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1answer
2k views

Feynman Path Integral Formula in Brian Cox' “A Night with the Stars” Lecture

The Youtube link keeps breaking, so here is a search on Youtube for Brian Cox' A Night with the Stars lecture. Pause the video on 40.32minutes. What you see he said is called Feynman's Path Integral. ...
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1answer
1k views

General procedure for Clebsch-Gordan expansions

I'm wondering if the Clebsch-Gordan series generalize to any orthonormal set of basis functions? If so, how would one go about deriving an expression for an arbitrary set of basis functions (perhaps ...
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1answer
507 views

Common Variables in Quantum Mechanics

I am an eighth grader (please remember this!!!) in need of some guidance in my school project on Quantum Mechanics, Theory, and Logic. I am attempting the create a graph of the Schrödinger Equation ...
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2answers
643 views

Is the free electron wavefunction stable?

The wavefunction of a free electrons is variously described as a plane wave or a wave packet. I am fairly happy with the wave packet, as it is localised. But if we change to the electron's rest ...
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1answer
144 views

Krauss operators for random unitary

Suppose I have a density matrix $\rho$ and I act on it with a unitary matrix that is chosen randomly, and with even probability, from $S = \{ H_1, H_2 \ldots H_N \}$. I want to write the operation on ...
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1answer
847 views

Relationship between nuclear spin and nuclear magnetic moment?

We know that nuclear magnetic moment can be expressed in terms of the expected value for nuclear spin as: $$\langle\mu\rangle =[g_lj+(g_s-g_l)\langle s_z\rangle]\frac{\mu_N}{\hbar}$$ (Cf. Krane), ...
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1answer
1k views

Degeneracy Pressure, What is it?

There has been numerous question, some violent even in physics@SE regarding PEP and EM forces. But what baffles me is what is degeneracy pressure? I know there are 4 fundamental forces- EM, gravity, ...
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1answer
260 views

Transpose Map Positive, But Not Completely Positive?

I am reading Introduction to Quantum Computing by Kaye, Laflamme, and Mosca. Here is a question I am struggling with: Exercise 3.5.6: Prove that the transpose map, which maps $\rho \mapsto ...
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1answer
628 views

Entanglement in time

Quantum entanglement links particles through time, according to this study that received some publicity last year: New Type Of Entanglement Allows 'Teleportation in Time,' Say Physicists at The ...
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38 views

Is the universe a quantum computer - is light speed barrier a computational constraint [duplicate]

Possible Duplicate: Is the universe a quantum computer - is light speed barrier a computational constraint Cross-posting this question, since physics.stackexchange has not provided any ...
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1answer
222 views

Entanglement and conservation

Is the following assertion sufficiently unique to merit a paper? Every absolute conservation law implies a corresponding form of entanglement, not just spin (angular momentum). Linear momentum ...
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2answers
144 views

Quantum entanglement of spin along multiple orthogonal axes

Picture an entangled pair of spin 1/2-spin particles with total spin 0. In the diagram, particle 1 of the pair is moving to the left (-y), and particle 2 to the right (+y). If a z-oriented SG$^*$ is ...
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4answers
507 views

Why does optical pumping of Rubidium require presence of magnetic field?

The optical pumping experiment of Rubidium requires the presence of magnetic field, but I don't understand why. The basic principle of pumping is that the selection rule forbids transition from ...
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3answers
2k views

Is the universe a quantum computer - is light speed barrier a computational constraint

There is currently a debate ongoing on leading maths blog Gödel’s Lost Letter, between Gil Kalai and Aram Harrow, with the former arguing that building a quantum computer may not be possible due to ...
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2answers
801 views

Connections between classical and quantum mechanics?

I've done basic or introductory mechanics at the level of Resnick and Halliday. I'm currently studying calculus of variations and the Lagrangian formulation of mechanics on my own. I read somewhere ...
2
votes
2answers
201 views

Is there an overlap between quantum dynamics and math of brownian motion?

Suppose you have dynamics of a coherent state. The state presents a normal distribution of finding the particle. Does anyone know of any attempts to connect modern advances in the probability theory ...
6
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2answers
154 views

Is ground energy of interacting fermions always higher that that of bosons?

Consider two systems, each made of $N$ particles. In both systems particles interact pairwise and the interaction is given by the same Hamiltonian for both systems. Any other constraints and/or ...
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3answers
343 views

Does no-cloning theorem implies a no-comparison theorem?

I was reading about no cloning theorem and it arose a thought experiment, if there were a way of compare quantum states (for being equal) then you could build a pseudocloning machine that searches for ...
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2answers
173 views

Hamiltonian of a water molecule bounded to a surface

Where can I find a way to construct the hamiltonian of a water molecule bounded to a surface? More generally,how can one write the hamiltonian of an atom bounded to a surface?
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2answers
513 views

Neutron electric dipole moment and $T$ symmetry violation

Our textbook (and other sources I have found) says that non-zero electric dipole moment of neutron would violate $T$ symmetry. They prove this statement by first assuming ...
6
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2answers
1k views

How is information related to energy in physics?

I recently attended a talk by Dr. Ravi Gomatam on 'quantum reality', where the speaker suggested, that conservation of energy is not a fundamental law, and is conditional, but the conservation of ...
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2answers
733 views

Deriving Planck's radiation law from microscopic considerations?

In the usual derivation of Planck's radiation law, the energies or frequencies $\omega$ of the oscillators depend on the measurements $L$ of the black body. The model is such that the only ...
3
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4answers
330 views

Are there more bosons or fermions in the universe?

The question is in the title: are there more bosons or fermions in the universe? Or is there the same number of bosons and fermions? I think there is the same number but I don't know why exactly.
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3answers
288 views

What is the Quantum equivalent of chaos on a classical system? (if there's any)

This is a question that bugging me around for some time now. It is not clear to me what is the meaning of a chaos if we consider a quantum system. What is the mathematical formalism (or the quantum ...
2
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2answers
84 views

Another question about Shankar's notation

I have another question on the notation in Shankar. I think it's sloppy, but I also may just be misunderstanding it. Again, this is at the very beginning of the math intro. He has: $$a\left| V ...
3
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2answers
457 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 ...
2
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4answers
283 views

How can new interpretations of QM help?

There is some current work on interpretations of quantum mechanics. How do you think can interesting results in that area help physics? Can it change quantum physics or make it easier? Which ...
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1answer
280 views

Conserved quantum observables from symmetries *with density matrix*

I’ve read Ballentine where he derives the conserved observable operators (momentum, energy, ...) from symmetries of space-time. Can I read up such a derivation in more detail somewhere else or even ...
2
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0answers
79 views

Factorization of fermionic scattering integral in 2d momentum rep

the scattering integrals for fermions involves both momentum ($k$) and energy ($k^2$) conservation and a nonlinear phase space factor of a distribution function $f(k)$. $$\begin{multline}I(k) = ...
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2answers
263 views

Question on notation in Shankar's Quantum Mechanics - math intro on vector spaces

I'm just beginning Shankar's 2nd edition Quantum Mechanics and having some trouble with notation. He defines his vectors as "$\left|V\right>$" . And with a scalar multiplier as "$a\left|V\right>$" . ...
4
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1answer
63 views

Tip of a spreading wave-packet: asymptotics beyond all orders of a saddle point expansion

This is a technical question coming from mapping of an unrelated problem onto dynamics of a non-relativistic massive particle in 1+1 dimensions. This issue is with asymptotics dominated by a term ...
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2answers
2k views

Why are scattering matrices unitary?

In Griffith's QM book, he introduces scattering matrices as an end-of-the-chapter problem. For a Dirac-Delta potential $V(x) = \alpha \delta (x - x_0)$, I've derived the scattering matrix and ...
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1answer
982 views

Derivation of angular momentum commutator relations

I'm trying to understand the derivation of the angular momentum commutator relations. How is $$[zp_y, zp_x] ~=~ 0?$$ How is $$[yp_z, zp_x] ~=~ y[p_z, z]p_x?$$