observables Definition and 112 Threads

Looking through this matrix approach to the quantum harmonic oscillator, http://blogs.physics.unsw.edu.au/jcb/wp-content/uploads/2011/08/Oscillator.pdf especially the equations m \hat{ \ddot { x } } = \hat { \dot {p} } = \frac {i}{\hbar} [ \hat {H} , \hat {p} ] I'm getting the impression...

hi PF I read the no-go Kochen theorem using 18 vectors projection (here). One attribute a value to an observable A: v(A) This function is supposed to be linear and verify v(AB) = v(A) v(B) so v(AB - BA) = v(A)v(B) - v(B)v(A) = 0 (v is a real number function) v must assign v(id) = 1 because v(A...

Homework Statement Is there a state that has definite non-zero values of E, L^2 and L_xHomework Equations L^2 and L_z commute with the Hamiltonian so we can find eigenfunctions for theseThe Attempt at a Solution I would say that there is a state with simultaneous eigenfunctions of L_x,L_y,L_z...

Hi guys! I have one question! I know that in quantum mechanics, observables must be in the form of operators. However, does that mean that all observables are quantized in quantum mechanics?

I'm having a gap in understanding the relation between them, and resolving my confusion is really appreciated. For example, the Hamiltonian operator, why do we call its eigenvalues energies? how do we actually measure it in the laboratory, quantum mechanically? And maybe I need a better...

¿Can´t matter that decoherence matters for 2 distinct observables simultaneously ¿ Maybe the measurement apparatus must been defined clasically in this case

Quantum mechanics says that physical observables are self-adjoint operators. Is this correspondence a bijection, ie can we realize any such operator as a physical observable? There are obvious practical concerns with physically realizing certain contrived operators. But are there any...

Hi Folks, I somehow cannot get the difference and have to admit that I am left confused. For a probability of measuring m with the operator M on state \Psi_i p(m|i) = <\Psi_i| M^{+}_m M_m |\Psi_i> = <\Psi_i| M_m |\Psi_i>. The average of an observable is defined as <O> = <\Psi_i| O...

Homework Statement I keep seeing this crop up throughout my QM course but i still don't understand what a "good" set of commuting observables would be. . Surely any set of observables that commute have to be a good set? I may just be stating the obvious but the way its phrased it makes me feel...

It's often said that gauge invariant local observables in quantum gravity must be relational. In classical gravity, relational observables are constructed with matter. LQG for the most part has not had matter, yet it has been said to have observables such as area or volume. Are these...

I have always been quite confused about the fact that any measurement MUST yield a real number. What says it must so? Don't we modify our measurement apparatus to yield something which is consistent with the theory. So coulnd't we just imagine having complex values for momentum and position. All...

I understand that the operators have to commute, and therefore that the measurement of one has no bearing on the measurement of the other. I know that H, L^2, and L_z form a CSCO for the H atom. Basically, I conceptually understand CSCO. Often though, in my class, we will be working on a...

I just have two questions relating to what I have been studying recently. 1) I know that the total energy and momentum operators don't commute, while the kinetic energy and momentum operators do. Why is this the case? (explanation rather than mathematically). 2) One form of the HUP says that...

Homework Statement Say I have two incompatible observables A and B. A has a finite number of base states say 4. How many base states should B have? Homework Equations Heisenberg's uncertainty AB - BA <> 0 The Attempt at a Solution I guess the answer is 4 as A and B basis states...

Alright... So I'm in an 'introductory' Q.M class in college right now, it's the only one that this two-year college has, so I don't have an upper division Q.M Profs to talk to about this, and since my prof is equally confused, I turn to the internet. Okay, so everyone knows that <ψ|Aψ> = <a>...

Homework Statement Observable \widehat{A} has eigenvalues \pm1 with corresponding eigenfunctions u_{+} and u_{-}. Observable \widehat{B} has eigenvalues \pm1 with corresponding eigenfunctions v_{+} and v_{-}. The eigenfunctions are related by: v_{+} = (u_{+} + u_{-})/\sqrt{2} v_{-} =...

One of the postulates of QM is that if the system is isolated from external interaction that its wave function will evolve deterministically. So just the measurements of observables are not deterministic. What is our reason for assuming that the wave function will evolve deterministically?

Hello, lets say I have Hamiltonian aproximation H(\vec{x}_a,\vec{p}_a) of gravitational interaction that can be used for n-body simulation of mass particles and photons. Spacetime curved by simulated particles would be asymptoticly flat. But I don't have a metric etc. All I have is evolution...

In classical physics, all observables commute and the commutator would be zero. However this is not true in Quantum Mechanics, observables like position and momentum (time and frequency/energy) don't commute. Why? Is it because the (probability) wave functions/forms of position and momentum...

Hi. Consider two isomorphic state spaces \mathcal{E}(1) and \mathcal{E}(2). The first belongs to a proton, the second to an electron and they both have the same spin. #Let B(1) be an observable defined on the first space, spanned by |1,u_{i}\rangle, eigenvectors of B(1) with eigenvalues b_i...

So my measurement of a quantum system is an eigenvalue of that operator. And we are not able to predict what eigenvalue we will get, even if we knew the precise state vector before we make our measurement. But QM allows us to calculate the average of all these eigenvalues, if we made an...

Some questions. Am I getting this basically right? What does a "state vector" look like? It looks like |α> or |β> But more than that... It is a complex vector in Hilbert space? Now, you get "observables" from state-vectors by performing operators on them. So the state-vector...

The following lecture from University of Oxford contains an explanation of the constancy of probability distributions for all observables when a system is in a stationary state: http://www.youtube.com/watch?v=0yvX4jhzblY#t=15m35s. However, the derivation of the vanishing amplitude does not...

Homework Statement Calculate the Eigenvalues and eigenvectors of H= 1/2 h Ω ( ]0><1[ + ]1><0[ ) Homework Equations I know H]λ> = λ]λ> The Attempt at a Solution I don't know if I am meant to concert my bra's and ket's into matrices, and if so how to represent these as matrices?

Homework Statement Is z|lm\rangle an eigenstate of L^{2} ? If so, find the eigenvalue.Homework Equations L_{z}|lm\rangle = \hbar m|lm\rangle L^{2}|lm\rangle = \hbar^{2} l(l+1)|lm\rangleThe Attempt at a Solution So since L_{z} and L^{2} are commuting observables, they have are...

Homework Statement Are the observables corresponding to the d/dx and x^2 operators complementary? Homework Equations none The Attempt at a Solution I know that if the operators do not commute then their corresponding observables are complementary. I just don't know how to show...

I heard in a conference that gravity forbids to construct local gauge invariants like Tr-\frac14 F^{\mu\nu}_aF_{\mu\nu}^a and only allows non-local gauge invariant quantities like Wilson Loops: Tr P e^{\oint_{\gamma} A_a dx^a}. Could someone explain me where does it come from? I have a basis...

i have been trying to learn a bit of quantum mechanics,this is some thing that has been bothering me , if the states of a system can be expressed as vectors in the Hilbert space,what is the motivation behind saying that physical observables can be given by operators?even then ,how can we say...

Hi, I am having a little trouble with the concept of finding out the maximal set of commuting observables. Suppose I have n commuting operators. Then the wavefunction I use must have n parameters also. For instance, L_{3}, L^{2} and H where H is the Hamiltonian and L is the angular momentum...

Hi, is it true that only Observables can be in Superposition? Meaning superposition of dead and live cats is invalid by some unknown mathematical reasoning? Jambaugh stated thus in the other forum that only observables can be in superposition. What's the mathematical or quantum logical proof...

Homework Statement On an arbitrary state, the observable \hat{A} is measured returning the result a. A compatible observable \hat{B} is then measured returning b. If \hat{A} is then measured again, is the same result a obtained? How about if \hat{A} and \hat{B} are not compatible...

I don't like the C^*-algebraic foundations of quantum mechnaics since it assumes that every observable must be bounded and self-adjoint. But most physical observables are not bounded. This came up in another thread, from which I quote some context: You are only missing implicitly...

Homework Statement In the proof that two observables \hat{O} and \hat{O}' commute iff they admit a common basis of eigenvectors, I'm not understanding one part. Homework Equations If {|a_k\rangle} is basis in Hilbert space we have: (OO')_{jk}=\langle...

let be A , B and C three non-commuting observables my question is how can one solve the problem with associative property ? i mean (AxB)xC will in general be different from Ax(BxC) and if we had 4 A, B ,C ,D instead of three the problem is even worse , how can anyone deal with it ...

some questions... => How are observables related to operators in quantum mechanics? => what is the physical significance of state funtion in quantum mechanics? => why are hermition operators associated with observables in quantum mechanics? => what is the physical interpretation of J...

exam practise question: what are the physical observables determined by the quantum numbers n, l, ml and ms of the electron in a hydrogen atom. most places just give the equation or the name not the physical observable determined. so is this right?:- n = principal number determines the...

I have to ask a question that looks very simple, and perhaps is very simple, but for some reason I can't answer it in a way that I'm satisfied with. If A and B are bounded self-adjoint operators that correspond to two different equivalence classes of measuring devices in the real world, and...

Homework Statement Theorem 5 of a text I've been reading that I downloaded from online (for interested parties, the link (a pdf) is http://bohr.physics.berkeley.edu/classes/221/0708/notes/hilbert.pdf) says that "If two observables A and B commute, [A, B] = 0, then any nondegenerate eigenket...

Question about measuring observables. If have 2 particle system the particle seperation Q=x1-x2 and total momentum P=p1+p2 are observables of the system as a whole and are commuting. How do you measure these observables. It would seem the only way to measure the separation is to measure the...

Homework Statement Two observables A_1 and A_2, which do not involve time explicitly, are known not to commute, \left[A_1,A_2\right]\ne 0 Yet they both commute with the Hamiltonian: \left[A_1,H\right]=0 \left[A_2,H\right]=0 Prove that they energy eigenstates are, in general, degenerate...

Homework Statement A particle that moves in 3 dimensions has that Hamiltonian H=p^2/2m+\alpha*(x^2+y^2+z^2)+\gamma*z where \alpha and \gamma are real nonzero constant numbers. a) For each of the following observables , state whether or why the observable is conserved: parity , \Pi; energy...

Homework Statement Consider a state |psi>, and two non-commuting observables A and B. Now study the following chain of measurements: (i) On |psi> a A [sic] measurement gives the result a1, and a subsequent measurement of B gives the result b2. (ii) On |psi> a B measurement gives the result...

Hi I am looking at Quantum Computation by Neilsen and Chuang at the CHSH inequality. Looking at the spin singlet state they make measurements of for example the observable Z1 and Z2-X1 and then find the expectation value of the product. I am slightly confused here because a) Z and X are...

For free quantum fields, there are two types of observables indexed by wave-number, \tilde{\hat{\phi}}(k), the Fourier transform of the local field, which can be written as a(-k)+a^\dagger(k), and projection operators such as a(k)^\dagger\left|0\right>\left<0\right|a(k), a(k_1)^\dagger...

The recent threads makse we want to as a simple question. How many considers the notion of a _fundamental_ "diff invariant observables" as a clear and unquestionable requirement of the future theory of QG? To me this far from clear from the conceptual point of view. It's not even clear...

What is the criterion to define the reference axes, since $S_x$, $S_y$ and $S_z$ correspond to different Pauli matrices?

I am quite new to Quantum Mechanics and I am studying it from the book by Griffiths, as kind of a self-study..no instructor and all... For a gaussian wavefunction \Psi=Aexp(-x^{2}), I calculated <p^{2}> and found it to be equal to ah^{2}/(1-2aiht/m) (By h I mean h-bar..not so good at...

[SOLVED] commutation of observables Homework Statement Prove: If the observables (operators) Q1 and Q2 are both constant of the motion for some Hamiltonian H, then the commutator [Q1, Q2] is also a constant of the motion. okay, first question.. am i being asked to prove that [[Q1, Q2], H] =...

Hi community, In the past weeks I'm busy ordering my thought on quantum mechanics. Somehow I really like to understand this part of physics, I don't want to just make a good exam. That's why I started writing down everything I know on quantum mechanics (from a mathematical point of view) and...

A variant of Schrödinger's cat experiment: Consider operators with eigenstates of the form |dead> + |alive>. If we could somehow measure such an operator we could kill a healthy person by just observing. :smile: So, what is going on here? Consider a simpler problem: A particle in...