Physics Forums - Quantum Physics

A question about optical theorem

ndung200790 — Wed, 22 May 2013 08:38:57 GMT

Optical theorem says that total cross section proportion to elastic scattering amplitude in the forward direction.Then if the target is absolutely reflective ''mirror''(in the case of quantum mechanics:scattering potential=infinity(r

The Quasi Classical Approximation(Landau Lifshitz)

aim1732 — Wed, 22 May 2013 06:09:27 GMT

So I was reading the Landau Lifshitz book on non-relativistic quantum mechanics and ran into this quasi-classical approximation they use at various points in the book.They have argued with an analogy that in the classical limit, the phase of the wave function will be proportional to the classical action S, like in optics.Can somebody give a more digestible insight than that?

And then in the quasi-classical chapter,they argue that the system is almost classical and the action integral(time-independent part)can be written as a power series of h.How do you justify that?

Spectrum of the Hamiltonian in QFT

unchained1978 — Wed, 22 May 2013 01:16:34 GMT

I know in ordinary QM, the spectrum of the Hamiltonian [itex]\{ E_{n}\}[/itex] gives you just about everything you need for the system in question (roughly speaking). So what happens to this spectrum in QFT where [itex]|\psi\rangle[/itex] is now a multiparticle wavefunction in some Fock space? I've been trying to understand this, but I don't yet have a clear grasp. Essentially, what's wrong with writing [itex]\hat H |\psi_{n}\rangle=E_{n}|\psi_{n}\rangle[/itex] in QFT where the psi's are now multiparticle states?

A modified double slit screen scenario- what would happen?

bcrelling — Tue, 21 May 2013 21:53:23 GMT

This scenario is identical to the classic double slit screen experiment except that the photon is at extremely high energy. The energy is so high that the photon's momentum maybe registered by a mechanical measuring device(i.e spring or accelerometer attached to a receiver).

At the moment of emission(before the photon has hit the screen/receiver) the emitter will recoil with the momentum opposite to the photon's. Surely this would give us information about the path of the photon before the photon is registered at the screen/receiver? What stops the wave function from being collapsed?

Double Harmonic Approximation IR intensties

DinosaurChemi — Tue, 21 May 2013 15:39:15 GMT

This feels silly asking but I have a question about units using the double harmonic approximation to determine IR spectral intensities. In the double harmonic approximation the intensity is given by
the square of the derivative of the dipole with respect to a normal mode coordinate times a scaling constant. Numerically this can be done by taking let say a 0.01 step along a mass scaled coordinates. The standard units of dipole are debye and mass scaled coordinates are unit-less so total units of debye squared. The scaling factor is Avagadro's constant divided by the speed of light squared. This gets me in units of times² current². Intensities are reported in km/mol. If anyone can give me a little help here I would appreciate it

Again the equation is:

[itex]I=(\frac{\delta \mu}{\delta Q})^{2}\frac{\pi N_{A}}{3c^{2}}[/itex]

A different BE statitics!

Shyan — Tue, 21 May 2013 14:49:47 GMT

I want to calculate the number of ways for putting [itex] N_1,N_2,N_3,...,N_i,... [/itex] bosons in energy levels with degeneracies [itex] g_1,g_2,g_3,...,g_i,... [/itex].
The particles are indistinguishable and there can be any number of particles in a state.
The level with degeneracy [itex] g_i [/itex] has [itex] N_i [/itex] particles in it.The first of this [itex] N_i [/itex] particles has [itex] g_i [/itex] states to choose.The second,again has [itex] g_i [/itex] choices and the same for all of them.So there are [itex] g_i^{N_i} [/itex] ways for putting [itex] N_i [/itex] particles in [itex] g_i [/itex] sates.But the particles are indistinguishable so their order is not important and so [itex] g_i^{N_i} [/itex] reduces to [itex] \frac{g_i^{N_i}}{N_i!} [/itex]. So the number of ways for putting [itex] N_1,N_2,N_3,...,N_i,... [/itex] bosons in energy levels with degeneracies [itex] g_1,g_2,g_3,...,g_i,... [/itex] is:
[itex]
\prod_i \frac{g_i^{N_i}}{N_i!}
[/itex]

But the above result will give us sth like Boltzmann distribution,not Bose-Einstein's and we know that the answer should be like below:
[itex]
\prod_i \frac{(N_i+g_i-1)!}{N_i!(g_i-1)!}
[/itex]

But what is wrong?
In deriving my formula,I assumed only that the particles are indistinguishable and don't follow Pauli's principle,the same assumptions made for bosons.So what was different?
Thanks

relation between mass and wave function

nil1996 — Tue, 21 May 2013 12:50:13 GMT

We know that electrons are nearly massless so their wave funtion is quite easily detectable.So is there any mathematical relation between the mass of the body and the intensity of the wave it exhibits?

thanks

A thought experiment of wavefunction collapse

backward — Tue, 21 May 2013 10:50:20 GMT

I propose a simple thpught experiment;
A scientist A measure the spin of an electron and finds it "up". After that he removes all evidence of his experiment and goes away, only to die in a road accident.
Another scientist, obviously unaware of the experiment done by A come and measures the spin of the same electron. Will B find the spin necessarily "up" or he will measure just any value "up" or "dpwn" with equal probability?
If the wave function collapsed by A is an objective reality, B should also measure the same value of the spin (up). Otherwise the experiment of B will be unaffected by the experiment of A, because he does not know anything about it.
Will anybody please enlighten me?

Trying to wrap my brain around entanglement-superposition

drschools — Mon, 20 May 2013 10:52:58 GMT

Could entangled superposition be something like the state of a mutiple choice question where 1)there are two or more options for answers (...the nature of a multiple choice question:approve:) before an answer is chosen by the observer-test taker and 2) the state of the question once the observer/test-taker answers the question. Before the question is answered the answers are in a kind of superposition - possibilities with accompanying probability. Once answered, the results take on a their differentiated "entangled" state... the one answer "chosen" determines the state of the other options - "not chosen". In binary quantum terms, "chosen" =1 , "not chosen" =0.

In this way the test taker (observer) defines the identity of the answers rather than the designer of the question...i.e. the focus of the answer is on which answer is chosen, not the content of the answer or even if it is right or wrong.

What think thee?

Quantum incompleteness?

TrickyDicky — Mon, 20 May 2013 10:52:30 GMT

Every so often discussions come up about completeness of quantum theory and I often can't see what their point is so I might be missing something.

Is it not possible for a theory to be incomplete and at the same time give very accurate predictions in its domain of applicability? Newton mechanics comes to mind as an example.

How is the Newtonian case in principle different from the quantum theory case besides the obvious the fact that the theory that would extend the domain of QM ("quantum gravity") hasn't benn found yet while in the Newtonian case we have relativistic mechanics?

intersection of supports for probability measures on a state

nomadreid — Mon, 20 May 2013 08:35:11 GMT

In the pre-print http://xxx.lanl.gov/pdf/1111.3328v3.pdf, the authors classify a state λ as
(a) a "real" state if all pairs of distinct probability measures μ₁(λ) and μ₂(λ) are distinct from one another,
(b) otherwise the state is "merely information".
The authors give some examples. However, I still do not understand what disjointness of supports has to do with a state's reality. Could someone restate this in "QM for Dummies" terms?
Thanks.

representation of linear operator using "series"?

V0ODO0CH1LD — Sun, 19 May 2013 23:11:46 GMT

I was looking into the progression of quantum states with respect to time. From what I understood the progression of a state ## \left|\psi(t)\right> ## is given by:
$$ \left|\psi(t)\right> = U(t)\left|\psi(0)\right> $$
I'm not sure if that's right. But it's okay if I haven't got that yet.. That was just to give some context to my actual question.

What is this representation of the linear operator ## U(t) ## at ## t = \epsilon ##, where ## \epsilon ## is an infinitesimal?
$$ U(\epsilon) = I - i\epsilon H $$
Where ## i ## is the imaginary unit, ## I ## is the identity matrix and I think ## H ## is the hamiltonian.
It also apparently has more terms of order ## \epsilon^2 ## and so on. What "series" is this? Is it some first order approximation of ## U(t) ##? What should I look into to understand where those terms are coming from?

Quantum Bayesian Interpretation of QM

Salman2 — Sun, 19 May 2013 19:55:38 GMT

Any comments (pro-con) on this Quantum Bayesian interpretation of QM by Fuchs & Schack ?:

http://arxiv.org/pdf/1301.3274.pdf

Wavepacket incident on a potential step

id00022 — Sun, 19 May 2013 11:26:09 GMT

Hello,
I am writing a Fortran 95 program to model the scattering of a wavepacket by a potential step of height V₀ at x=0. My wavepacket is formed by the superposition of numerous travellling waves of different k values. The wavepacket has the dispersion relation ω(k)=k². I want the wavepacket to be in its undispersed state at t=0 at a start position x₀. Therefore each component wave is composed of an incident wave, reflected wave, and transmitted wave.

At x≤0 :
ψ(x,t)=A(e^{i(k(x-x₀)-ωt)} +[itex]\frac{k-k'}{k+k'}[/itex]e^{-i(k(x+x₀)-ωt)})

At x>0 :
ψ(x,t)=A[itex]\frac{2k}{k+k'}[/itex]e^{i(k'(x-[itex]\frac{k}{k'}[/itex]x₀)-ωt)}

The factor of [itex]\frac{k}{k'}[/itex] in the bottom equation was found analytically to ensure continuity in the wavefunctions at the boundary. Well, at least that's what I thought: It works as long as E>V₀ otherwise there is discontinuity. Can anyone help me as to why? I dont think this is a Fortran programming problem, but more of a physics one...

Quantum Behavior As Extreme Classical Behavior

sanman — Sun, 19 May 2013 06:54:09 GMT

Why can't quantum behavior be explained as an extreme version of classical behavior?

For instance, the idea of a small quantum particle being in superposition could be explained by that particle switching between 2 or more states at an extremely high frequency. How high a frequency? Well, on the order of a Planck Length or Planck Unit.

The only addendum to classical behavior that would be required would be non-locality or tunneling (ie. macroscopic objects are too big to tunnel, but quantum-sized objects are small enough to squeeze through the cracks)