Qm Definition and 1000 Threads

Hi guys I am reading a book, where they use vector expressions a lot. In it they write {\bf{M}} = \sum\limits_{\psi ,\psi ',\sigma ,\sigma '} {\left\langle {\psi '} \right|\left\langle {\sigma '} \right|{\bf{m}}\left| \sigma \right\rangle \left| \psi \right\rangle a_{\psi ',\sigma '}^\dag...

Homework Statement Hi guys As we have discussed earlier, we can represent some operator in an arbitrary basis by the use of the 1-operator: T = \hat{1} T \hat{1} = \sum\limits_{\sigma_a,\sigma_b } {\left| {\psi _{\sigma_a} \left( {r_i } \right)} \right\rangle...

In thermodynamics, two variables A and B are uncorrelated when: <AB>=<A><B> where <> are the expectation values in thermodynamics (for example calculated using Boltzmann distributions). What are the conditions in quantum mechanics for two operators to be uncorrelated, i.e...

I'm pretty confused by the rules regarding the total energy, the kinetic energy, and potential of a QM system. Does the total energy have to be positive or greater than zero? And if so, why not? I don't really understand what it means to have a negative total energy of a system I guess. I...

Hey, I am a second year physicist, and I have only recently been introduced to the postulates of QM. I am still trying hard to understand how the original inventor's of QM came up with the third postulate. Postulate 3 says the classical combination of dynamical variables gives the correct...

Homework Statement Hi Say I have the kinetic energy operator denoted by T(ri) for the particle i. I wish to represent it in some \left| \sigma \right\rangle -representation. My book says it is given by T = \sum\limits_{\sigma _a ,\sigma _b } {T_{\sigma _a ,\sigma _b } \left| {\psi...

Why do we have to use operators in QM?

Hi all, Please can you suggest a good book of quantum mechanics?

I should know how to do this, but I've been getting a bit confused. Can you solve the particle in a box problem considering that the particle is a massless photon? I'm not so sure on how to write the Hamiltonian correctly for this problem. EDIT: Ok, to add some information, I'm actually looking...

Homework Statement This is a quick one, which I apologize ahead of time for not writing this out more neatly. The parentheses denote subscripts. I have a system of two particles, which are in a superposition Psi(one) + Psi(two). The energy of particle one is E(1) and of particle two is...

Is QM really applicable to everyday life in the macrocosm? If it is, how? And does QM say there are no causes, only effects. So, for example, in th e real world (macrocosm), there is a set of possibilities A, B, and C, and causal factors x, y, and z. However, x is an unknown or hidden...

Hi, As I'm sure you are all well aware, QM is all about probability in your measurement. When we scale up to the classical world, the probabilities disappear, we calculate one specific state for your system given a certain set of starting conditions. What I was wondering is, is the QM world...

Homework Statement Pro #2 if you click on this link. http://s1104.photobucket.com/albums/h332/richard78931/?action=view&current=hw4.jpg Homework Equations , The Attempt at a Solution Click here http://s1104.photobucket.com/albums/h332/richard78931/?action=view&current=2a.jpg...

Homework Statement A free particle at time t=0 has the Gaussian wave-packet: \Psi(x,t=0)=Ae^{-\tfrac{x^2}{2\sigma^2}}e^{ik_0x} (a) What is A? (b) What is the probability of measuring a momentum in the range between p and p+dp? Homework Equations (a) \int^{\infty}_{-\infty}|\Psi(x,t)}|^2...

Hello all. As I understand it, there's somewhat of a divide in the scientific community (basically between chemists and physicist) around the topic of solutions to the SE (or KS eqn) that give fractional occupations of molecular or KS orbitals. I myself see no physical reason why probability...

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...)

Hi all, I'm posting this here and not in the Beyond the Standard Model forum because my question is not very precise and I don't know anything substantive about strings or LQG. That being said I will launch into my inquiry. It's my understanding that the need for a theory beyond the...

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, I am reading this article for homework about a ring in a megnetic field. It starts off by giving a hamiltonian (an adiabatic part -never mind) H_{0}= \frac{1}{2M} [ \Pi -A]^{2} -\mu B( \phi) \cdot \sigma A- is a known operator where \Pi=\frac{1}{2a} \frac{d}{d \phi}...

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 :)

Hi there! I'm solving the dirac equation to get the fine structure hamiltonian of the hydrogen atom. In the hamiltonian there is this term: \frac{\hbar ^2 e}{4m^2c^2}\frac{dV}{dr}\frac{\partial}{\partial r} This term gives rise to some difficulty because it is not hermitian. So Darwin...

The question: Consider extremely fast alternating energy and omega-ness measurements—so fast that you can neglect the much slower time evolution produced by the Hamiltonian. Draw and explain the branches of the probability tree for the case where the first measurement is an energy measurement...

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...

I claim that an experimental demonstration of interference using single particles like photons is also an experimental demonstration of the validity of QM on the macro scale. The idea is that any which path information will destroy the interference pattern. Formally, the visibility of the...