Qm Definition and 1000 Threads

Homework Statement I was wondering why is the ground state wave function of a particle in an infinite square well allowed? If you drawn it out on a graph, it is one-half of a full sine wave. But the conditions for an acceptable wave equation is one that is continuous (yes) and...

Homework Statement [PLAIN]http://img716.imageshack.us/img716/8330/werhc.png Homework Equations The Attempt at a Solution My question is what do I need to prove to show that the wave function is acceptable. So far all I can think of is showing that the wave function is 0 outside...

Homework Statement A spin 1/2 particle of mass m is described by the Hamiltonian: H = p^2/(2m) + 1/2 mw^2 x^2 + g * x * sigma_x, where sigma_x is one of the Pauli matrices. Homework Equations The Attempt at a Solution I have no idea where to start. It's obvious that the harmonic...

For a particle in a potential V(x), calculate [H,p] H = \frac{-\hbar^2}{2m}\frac{\delta^{2}}{\delta x^{2}} + V(x) p = -i\hbar \frac{\delta}{\delta x} [H,p] = Hp - pH = \frac{-\hbar^2}{2m}\frac{\delta^{2}}{\delta x^{2}} * -i\hbar \frac{\delta}{\delta x} + V(x)-i\hbar...

Homework Statement Given an initial ave function \Psi(x) at t=0, and a complete set of energy eigenfunctions \varphi_{n}(x) with corresponding eigenenergies E_n for a particle, and no other information, in therms of the given find: [b]a. Find the state of the particle at a later time...

Why are theories of Quantum Mechanics and Relativity not possible to combine? I read this on wikipedia and heard this on a documentary on TV.

Greetings, I know that position state ket is a continuous state ket satisfying X|x> = x|x>. There is however one notation I don't understand. What does it mean when we label the position ket with a discrete index and then use these to expand operators as <x_i|H|x_j>? What does it generally...

What are the actual problems of joining these two theories? (I've heard various people say that the equations 'fail' or 'blow-up', but I want to know exactly what happens...)

In the standard derivation of the virial theorem, one assumes to be working in the energy basis. One then gets <T> = n/(n+2) <H>. This relation doesn't hold for the continuous spectrum of Coulomb potential where <T> > 0, <H> > 0, n/(n+2) = -1. So, where in the derivation did we use the fact we...

I'm still enjoying Daniel T. Gillespie's "A Quantum Mechanics Primer". It includes six postulates of quantum mechanics which are very similar to sets I've found in other texts, as well as by internet-searching "quantum mechanics postulates": 1. Identifying the state of a system with a...

Consider the double-slit experiment using a low-intensity source of monochromatic photons: If the intensity is low enough, one can observe the photons, one at a time, slowly developing an interference pattern on a photographic plate. The interference pattern, over time, resembles more and...

Hi All, Let me see if I can put my doubt in words appropriately... Imagine a source of EM radiation, say a laser beam, and suppose you are running against the laser's direction, i.e., photons go to positive x and you to negative x direction, for instance. From the POV of SR, light does...

I just finished the first 4 chapters of Sakurai's Modern qm, and now I'm beginning to learn purterbation method and scattering theory, but from the feedback it seems that many people are quite unsatisfied with Modern qm on these parts. Could you guys recommand a nice book on perturbation and...

I'd liked to know whether the postulates of standard QM are still valid in Relativistic QM By postulates I mean what is ussually stated in texbooks as follows 1)Physical states are determined by a vector in sate space E 2)A measurable physical quantity A is described by an observable A acting...

My understanding is that any uniform motion ( according to relativity) can be considered stationary. For example if object A is moving at a constant velocity, it is as legitimate to say that it is stationary as to say that it is in motion. Why cannot a photon, moving at the speed of light and at...

Acc. to QM no two particles can be in the same state at the same position at the same time, but how does that reconcile with SR where two observers do not agree on simultaneity? Do some observers see baryonic stuff violate this postulate?

hi, I am a novice to quantum mechanics and get a lot of troubles with operators. I cannot explain why: - why QM uses operators for observables such as position, momentum, energy, ..ect, but classical physics does not? - what are physical interpretations of operators? - why are operators needed...

Hi all, I have a confusion right now. To the truth is, I have been studying QM for some years, but somehow, some of its concepts are still not really clear for me. I understand that one of components of QM interpretation that generally accepted now is the Born postulate that...

One of the most classical and verified principles of physics is that entropy never decreases. E.g. gas occupying half of a 1L container will quickly disperse quite-evenly throughout the container. It seems however, that QM easily allows momentary violations of this principle. For instance...

Discuss :)

Homework Statement So we have an observable K = \begin{bmatrix} 0 & -i \\ -i & 0 \end{bmatrix} and its eigenvectors are v1 = (-i, 1)T and v2 = (i, 1)T corresponding to eigenvalues 1 and -1, respectively. Now if we take the outer products, we get these... |1><1| = (-i, 1)T*(i, 1) =...

Hello everyone! I would like to ask you guys what the prerequisites for learning quantum mechanics are? Especially in mathematics, what are the mathematical topics I need to grasp before possibly trying to learn quantum mechanics? Generally, I know that linear algebra and calculus are needed...

Hi I been reading on some of the different interpretations of QM (Many Worlds, Copenhagen, polit wave, etc.), and I still can't figure it out: Are these interpretations beneficial to QM? Have we ever gained any new insight from these?

I will eventually learn both, but as far as mathematics goes (not concept,) which is easier to learn, Quantum Mechanics or General Relativity? I really am asking in terms of mathematics, because I know Quantum Mechanics has more application but I am not using that as a factor. thanks!

Homework Statement What are the possible results and their probabilities for a system with l=1 in the angular momentum state u = \frac{1}{\sqrt{2}}(1 1 0)? What is the expectation value? ((1 1 0) is a vertical matrix but I can't see how to format that) Homework Equations The...

The thing we call dark matter its really just dark gravity. we don't know if its matter or something else, for example: -in ST it could have something to do with parallel universe -in QM maybe some quantum fluctuation in the higgs field -in GR it some matter that doesn't interact with...

Hi, I am currently working through Griffith's textbook on quantum mechanics. I was just wondering if there are any animations or videos that work along with griffiths and clarify certain concepts. Thanks.

Hi, I'm reading Shankar's Principles of QM and I find it not very clear on how exactly should I change basis of operator. I know how to change basis of a vector so can I treat the columns of operator matrix as vectors and change them? Or is it something else?

what do the non-diagonal components of a density matrix tell us about the mixed state we are in?

For the operator L(z) = -ih[d/d(phi)] phi = azimuthal angle 1) write the general form of the eigenfunctions and the eigenvalues. 2) a particle has azimuthal wave function PHI = A*cos(phi) what are the possible results of a measurement of the observable L(z) and what is the...

Hi all, I'm studying Quantum mechanics and there seems to be a lot of conceptual concepts involved. Some of it can be a bit dry and I find myself getting easily distracted. What is the best way to study such a subject? Any feedback would be greatly appreciated. Thanks.

Greetings, In trying to even ask this question it’s obvious I don’t understand enough about the topic of QM and light. Here is my attempt at my question: If I shine a laser beam at a target or sensor – the electronics every time detects the beam. How do the Schrodinger wave equation...

Does the notion that a mechanical resonator following the laws of quantum mechanics imply that a similar logic should be used to understand micro and macro events? If there is no border, then why should the logic be different? In other words, if macro events are based on QM, yet they are...

My friend and I were talking , and my friend said that the laws of QM break down at large scales , But i was thinking that they don’t break down the probabilities just become smaller and it becomes harder to use QM . So what do you guys think

Please tell me how conservation of energy and mass apply in QM. I want to confirm something I read somewhere about QM not conserving energy.

Homework Statement I'm trying to follow the solution to a homework problem in QM, and I don't fully understand this step. Where does the factor (2\pi)^3 come from? \int...

hello, is there a reference book in linar algebra that covers topics found in studying quantum mechanics like: vector spaces, operators , matrix , eigenvectors and eigenvalues. i mean not a physics book, i want a mathematics book that talks about these notions and others in an abstarct way...

A buddy of mine asked me to explain QM. I don't by any means tout myself as having any sort of worthwhile knowledge about it so I was a little surprised he asked me. But nevertheless, I explained it to the best of my ability. I'm hoping you guys can tell me if I've royally messed anything up...

So I was checking out some cool videos on youtube of helium in superfluid state and I have a question about it. How exactly does this superfluid have both zero and non-zero viscosity at the same time? The evidence seems pretty clear that it exhibits zero viscosity since it forms a Rollin...

I always thought superposition principle is a consequence of the linearity of Schrodinger's equation, but it's not, instead it's a fundamental principle in QM according to some references I read recently. However I did not find any detailed explanation about this, could someone kindly explain to...

Dear users, I wonder if there is anybody who can give me a hint on how to handle the following situation: In the 2+1 dimensional Klein-Gordon equation with coordinates (t,x,y), I use as initial condition for \Psi(x,0) a spherically symmetric Gaussian. The relativistic dispersion relation...

Homework Statement For l=1 the angular momentum components can be represented by the matrices: \hat{L_{x}} = \hbar \left[ \begin{array}{ccc} 0 & \sqrt{\frac{1}{2}} & 0 \\ \sqrt{\frac{1}{2}} & 0 & \sqrt{\frac{1}{2}} \\ 0 & \sqrt{\frac{1}{2}} & 0 \end{array} \right] \hat{L_{y}} =...

We've been watching this development taking shape ever since the tentative Gambini Pullin papers about it in 2006. It represents a fundamentally new way to address the problem of interpreting Quantum Mechanics. One person who worked on this back in 2006, with Gambini and Pullin, used to post...

In BLACK HOLES AND TIME WARPS by Kip Thorne there is a fascinating discussion about how electron degeneracy pressure fights gravity in dense stars, beginning on page 146. He says the following (abbreviated excerpts) : "..Quantum mechanics insists that when already dense matter is compressed...

Hi All, In quantum mechanics, related to photon, we have these two equations as valid ones: E = h x f p = h / lambda But we have in vacuum the dispersion relation c = lambda x f. 1) How these relations change when the dispersion relation change ? 2) Is it universally correct to...

The algebraic formulation of quantum mechanics (and related stuff, like quantum thermodynamics & dynamical systems etc.) via C*-algebras provides a viewpoint based mostly on abstract functional analysis. However, I've yet to see a working application of this approach, i.e. an example of a...

Hi all I have some questions regarding interpretations of QM. I am not a physicist or mathematician, although I have good general knowledge of science. I'm a philosopher with an interest in the relationships between science, religion and metaphysics. I am trying to link together many...

Retrocausality solves QM problems?? Does retrocausality successfully solve the problems of QM? This recent paper seems to claim it does. http://arxiv.org/abs/1001.5057 Comments, anyone? Also what is the relationship of retrocausality and collapse? TIA Jim Graber

Off pg 977 MTW Gravitation : Consider a classical radiation field whose associated quantum mechanical particles have integer spin S, and zero rest mass. Resolve that radiation field into spherical harmonics - i.e. into multipole moments. all components with l<S will vanish; in general those...

Hi I want to take a year long QM squence at my school but the prereqs is a year long sequence in E&M. I was wondering what skills are picked up from E&M that is used in QM. I have taken modern physics which had light exposure to QM and I did not see much drawn from what little E&M i know...