State vector Definition and 41 Threads

https://en.wikipedia.org/wiki/Observability I am studying observability and I try to get some intuition on the topic. Given the observable matrix, we can find the null space. However, the vectors of the null space are states but this differs from the definition of what a state vector of a...

In the section 8-2 dealing with resolving the state vectors, we learn that |\phi \rangle =\sum_i C_i | i \rangle and the dual vector is defined as \langle \chi | =\sum_j D^*_j \langle j |Then, the an inner product is defined as \langle \chi | \phi \rangle =\sum_{ij} D^*_j C_i \langle j | i...

As a simple example, the probability of measuring the position between x and x + dx is |\psi(x)|^{2} dx since |\psi(x)|^{2} is the probability density. So summing |\psi(x)|^{2} dx between any two points within the boundaries yields the required probability. The integral I'm confused about is...

If I'm using the basis vectors |u> and |r> for two polarisation states which are orthogonal in state space, I've seen the representation of a general state oriented at angle theta to the horizontal written as $$\lvert\theta\rangle = \cos(\theta) \lvert r \rangle + \sin(\theta) \lvert u...

Is it possible to expand a state vector in a basis where the basis vectors are not eigenvectors for some observable A? Or must it always be the case that when we expand our state vector in some basis, it will always be with respect to some observable A?

In the four-observation method of Gauss for orbit determination, the right ascension and declination of an asteroid is observed at specified times, and the heliocentric position of Earth is obtained from tables (or JPL Horizons) for those same times. I can follow the procedure to the point...

Hi physicsforums, I am an undergrad currently taking an upper-division course in Quantum Mechanics and we have begun studying L^2 space, state vectors, bra-ket notation, and operators, etc. I have a few questions about the relationship between L^2, the space of square-integrable complex-valued...

To me the state vector represents the following... 1) The number of elements in the state vector is the number of possible outcomes. Call that number n. 2) The value of each element in the state vector is the probability amplitude associated with that outcome. If that is true, then it seems to...

By the Principle of Superposition, a state vector can be defined as pic.01 also, the state vector can represent a wave function in a continuous case as pic.02 My (1) question is, in pic.03, why the state vector can be pulled out from the integral? I have an idea but I think it should be...

Interesting new work on the link between quantum state vectors are physical states: Can different quantum state vectors correspond to the same physical state? An experimental test Daniel Nigg et al 2016 New J. Phys. 18 013007 Abstract A century after the development of quantum theory, the...

Homework Statement Given an initial distribution state vector that represents the probability of the system to be in one of its states. Also given a Markov transition matrix. How to calculate the state vector of the system after n-transition? Homework Equations Assuming the initial state...

Hi all, I am reading the book "Emperor's New Mind" and have a question related to time asymmetry in state vector reduction (p.458) in quantum mechanics. Consider the following situation, as presented in the book: Suppose I have closed room with a lamp L, which emits light in some fixed...

Homework Statement Find a state vector |v> ∈ ℂ^2 such that if a measurement of δx is made on a qubit in this state, then the prob. of obtaining the value of +1 in the measurement is 9/10. What is <δx> in this case? Homework Equations State Vectors: https://en.wikipedia.org/wiki/Quantum_state...

The state, ##| S\rangle##, say, of a system is represented as a vector in a Hilbert space. ##\psi (x, t)## is the representation of the state vector in the position eigenbasis; ##\psi (p, t)## in the momentum eigenbasis et cetera. That is, ##\psi (x, t) = \langle x|S\rangle##; ##\psi (p, t) =...

Homework Statement I am given this state, which is the result of a lamba particle decaying into a proton and neutral pion. Initial j = 3/2. The final state can theoretically be written as: I have already determined that: alpha_p = Sqrt[2/3] beta_p = Sqrt[1/3] alpha_d = -/+ Sqrt[2/5]...

Homework Statement A satellite is orbiting Earth with a period time of T=110 min. At the ascending node, the state vector of the satellite is rAN =[4500 7100 ?]T km At the northernmost latitude, the state vector of the satellite is rn=[1700 ? 7000]T km. The question marks imply that the...

Why does the magnitude of a ket vector not matter? The motivation appears to be that a state vector only can decribe a particle, or no particle. But why shouldn't the magnitude of ket vectors not be used to represent the density of the particles, the average number of particles? I'm am fairly...

"Let’s begin by labeling the possible spin states along the three coordinate axes. If A is oriented along the z axis, the two possible states that can be prepared correspond to σz= ±1. Let’s call them up and down and denote them by ket-vectors |u> and |d> . Thus, when the apparatus is oriented...

Often ignored, but turned out to be a problem when trying to compute the commutator of position and spin. Pauli matrices clearly acting on two dimensional vectors while position on infinite dimensional vectors. But a system is described as a single state vector in Dirac notation. A system can of...

The Schrödinger equation rotates the state vector in Hilbert space continuously (i.e. without jumps). This makes sense for individual systems, but I'm finding this hard to reconcile with coupling or entanglement. For example, consider how Schrödinger's cat paradox is typically presented (in...

Consider 2 atomic orbitals with wave function a: σ(r), b: μ(r) in a diatomic molecules. σ(r) (or μ(r)) is localized around an atom a (or b) and is relevant for the discussion of the molecular orbital. These orbitals are orthogonal and normalised. The creation operators are x, y and vacuum, |0>...

1. In the many statements of the QM postulates that I've seen, it says that if you measure an observable (such as position) with a continuous spectrum of eigenvalues, on a state such as then the result will be one of the eigenvalues x, and the state vector will collapse to the...

What is the state vector of the system after measuring a degenerate eigenvalue? Surely there are infinitely many vectors of norm 1 that it could be since the degenerate eigenvector span a 2d subspace. Say that we e.g. have a system where the operators eigenvalues are degenerate such that...

Homework Statement Suppose that the initial vector P0 is not given and instead we are given that at time t=299 the state vector is P_299=[.1 .1 .8]. Than find P_300, the state vector at time t=300 Homework Equations I also know from the problem it is referencing that the transition...

Hi, My understanding that one of the postulates of quantum mechanics is that the vector describing the quantum mechanical state of a system evolves in a linear fashion. My question is how this can be reconciled with systems where the system evolves in a non-linear fashion for example systems...

According to this review: http://lanl.arxiv.org/pdf/quant-ph/0508202v1.pdf A classical EM plane wavefunction is a wavefunction(in Hilbert space) of a single photon with definite momentum(c.f section 1.4) , although a naive probabilistic interpretation is not applicable. However, what I've...

Hi Everyone, I am working on a state space model for an electromechanical system. Part of the issue is the internal state vector ends up having interdependencies. Take the following state vector as an example: \begin{equation} X = \begin{bmatrix} x_1\\ x_2\\ x_3\\ x_4\\ x_5 \\ x_6...

If we assume a system (pure for now) is in a state described by a single state vector, how can you determine the momentum? The momentum of a wavefunction is simply -i times the gradient, but that's for a continuous function. In the hilbert space representation of psi as a ket vector, what does...

I'm attempting to find a system of ODEs for a vehicle in motion that undergoes acceleration due to the gravitational pull of different bodies in space. It has an initial velocity, but doesn't undergo any change in acceleration due to thrust. This vector represents its motion...

A particle is in a state for which the probabilities are P(L_{z} = 1) = \frac{1}{4}, P(L_{z} = 0) = \frac{1}{2}, and P(L_{z} = -1) = \frac{1}{4}. Show that the most general normalized state with this property is: |\phi> = \frac{e^{i \delta_{1}}}{2}|L_{z} = 1> + \frac{e^{i...

I believe Dirac spinors are not in any Hilbert space since it has no positive definite norm. However one QM axiom I learned told me any quantum state is represented by a state vector in Hilbert space, so what is happening to Dirac spinor?Or is it just that the axiom is not for relativistic QM?

Homework Statement I have a state vector: |\psi\rangle=3|+\rangle+4|-\rangle And I should normalize it. + and - are states. And I'm confused. How to normalize this if I have numbers here. Since we can write the vector state: |\psi\rangle=\sum_k c_k|e_k\rangle where |e_k\rangle are basis...

Homework Statement Two identical bosons are found to be in states |\phi> and |\psi>. Write down the normalized state vector describing the system when <\phi|\psi>\neq0.Homework Equations The normalized state vector for two bosons with <\phi|\psi>=0, using the fact that...

If A is a matrix that represents an observation and v is a vector that represents a system state before being observed - and v is not an eigenvector of A - is there any physical significance to the product Av? At first I thought it was what v would become after the observation (I was reading a...

I have been studying the theoretical framework of quantum mechanics in an attempt to have a working understanding of the subject, if not a comprehensive one, and I have hit upon the following stumbling block. Now, given that the orthogonality of states is preserved with time, it is easily...

If we have an operator A which operates on some state described by vector x the result is a new vector y A |x> = |y> My question is: is the new vector y considered to be a different state vector in the same vector space as x or is it considered to be a vector in an entirely different vector...

I made a post in the quantum mechanics section, but it hasn't gotten any replies, so I'll try again here. This isn't strictly a homework/coursework problem, but something that I really want to know. Homework Statement As a high school student, I only have a basic understanding of quantum...

Hi all, I'm a newbie to this forum and as a high school student, I only have a basic understanding of quantum mechanics, but here's something that I really want to know. My question is, if I know the state vector of a quantum particle in the position basis, how do I transform it to the...

Hello everyone, confused. the directions to this problem are the following: Find the steay-steat vector, and assuming the chain starts at 1, find the probablity that it is in state 2, after 3 transitions. well i got the problem and i got the S0 to S3, because it said after 3 transitions, is...

Hi, Does anyone knows how to calculate the eccentric anomaly E, or the mean anomaly M, given a state vector? Regards, Kepler

Hi, I have sort of a problem: I have a routine to calculate the geometric place ( the state vector ) of the bodies in our solar system ( from Paul Heafner - you probably know it ). But the problem is that the results are referred to the J2000 epoch frame. I was trying to convert the vector...