quantum system Definition and 37 Threads

Very simple question: for a two-state quantum system (qubit), is its state space a two-dimensional Hilbert space over the complex field ##\mathbb C## isomorphic to ##\mathbb C^2## or is it ##\mathbb C^2## itself ?

This is about the paper by Greiter: https://arxiv.org/pdf/cond-mat/0503400.pdf Greiter argues that local electromagnetic gauge symmetry cannot change the state of a quantum system. On the other hand, in QED charge or particle conservation (if energy is too low to produce particle-antiparticle...

My main question here is about how we actually justify, hopefully fairly rigorously, the steps leading towards converting the sum to an integral. My work is below: If we consider the canonical ensemble then, after tracing over the corresponding exponential we get: $$Z = \sum_{n=0}^\infty...

In quantum mechanics if I repeat a measurement of the same observable in succession I get the same quantum state if it is not a degenerate state. If I make the system under consideration interact with another quantum system and meanwhile keep measuring it what happens? Does the system not...

In the other thread of a similar name it was stated, and probably rightly so, that I wasn't using rigorous terminology or that I wasn't using them in a rigorous way. While I was making certain assumptions about the ability to interpret the 'jargon' I was using, it seemed to be a serious...

Continuing the discussion in the 'Assumptions of Bell's Theorem' thread, I'm hoping to explore the question of the location/position of the QM system prior to measurement. I may have some bias or underlying assumption that is affecting the conclusion that I am drawing and, by exploring this...

Summary:: Find the ratio of the number of particles on the upper level to the total number in the system. Consider an isolated system of ##N \gg 1## weakly interacting, distinct particles. Each particle can be in one of three states, with energies ##- \varepsilon_0##, ##0## and...

If a system is in an eigenstate of the hamiltonian operator, the state of the system varies with time only with a "j exp(w t)" phase factor. So, the system is in a "stationary state": no variation with time of observable properties. But the system could in theory (for what I understand) be...

What is nonlocality? How could a quantum system (like a superposition - is that right?) "know" an interaction will take place? Source...

I’ve never worked with a quantum system with more that two states 1, -1, and I’ve just gotten this homework problem. I'm not sure what it means. Does this mean it has five states? Why are there two 0’s and two 1’s?

How to prove the dipole moment of an isolated quantum system in isotropic space is identically equal to zero, unless there exists an accidental degeneracy. Thanks in advance

If a wave function could be assigned to a whole galaxy, would its mass spread along the wave? Could this account for the anomalies in our calculations for galactic spin?

Homework Statement Sakurai, problem 1.11 A two-state system is characterized by the Hamiltonian $$ H = H_{11} | 1 \rangle \langle 1| + H_{22} | 2 \rangle \langle 2| + H_{12} \left[ | 1 \rangle \langle 2| + | 2 \rangle \langle 1| \right] $$ where ##H_{11}##, ##H_{22}##, and ##H_{12}## are real...

In the algebraic approach, a quantum system has associated to it one ##\ast##-algebra ##\mathscr{A}## generated by its observables and a state is a positive and normalized linear functional ##\omega : \mathscr{A}\to \mathbb{C}##. Given the state ##\omega## we can consider the GNS construction...

Quantum decoherence means that when a quantum system interacts with its environment, coherence is lost, which means that all the density matrix becomes diagonal after the interaction. I never understood why it is so, but I get a clue here...

I'm trying to understand the concept of uncertainty in relation to derivatives for a large quantum system, i.e. one with many degrees of freedom. When is it true that σE/σt ~ dE/dt? ---- 'σ' is the uncertainty First, I know there is no time operator in quantum mechanics. I'm not sure how to...

Homework Statement I have to find the matrix system of Sx, Sy , and Sz using the given information: 190899[/ATTACH]'] Homework EquationsThe Attempt at a Solution for attempting Sx: Ignoring the ket at the bottom, I would get Sx|+> = +ħ/2[[0,1],[1,0]] but my question here is, does the ket at...

Homework Statement |1> and |2> form an orthonormal basis for a two-level system. The Hamiltonian of this system is given by: \hat{H} = \epsilon \begin{pmatrix} 1 & i \\ -i & 1 \end{pmatrix} a.) Is this Hamiltonian hermitian? What is the significance of a hermitian operator? b.) Find the...

To start off I'd like to apologize ahead of time for the grammatical errors and lack of eloquence that are sure to follow, it's the middle of the night and my mind is wandering but my cognitive capacity to express my self is pretty low at this time. With that out of the way, I'd like to ask...

By reading Heinz-Peter Breuer: A Piece Wise Deterministic Process (where you have a deterministic time-evolution + a jump process and which is just a particular type of stochastic process) may be defined in terms of a Liouville master equation for its probability density : Where the first...

If I have an arbitrary quantum many-body model, what is the method to calculate the the conserved quantities if the model is integrable. If it is hard to explain, can you recommend some relevant books for me? Thanks a lot!

Homework Statement A quantum system has Hamiltonian H with normalised eigenstates ψn and corresponding energies En (n = 1,2,3...). A linear operator Q is defined by its action on these states: Qψ1 = ψ2 Qψ2 = ψ1 Qψn = 0, n>2 Show that Q has eigenvalues 1 and -1 and find the...

Homework Statement Consider an electron bound in a hydrogen atom under the influence of a homogenous magnetic field B = zˆB  . Ignore the electron spin. The Hamiltonian of the system is H = H0 −ωLz ,where H0 is the Hamiltonian of the hydrogen atom with the usual eigenstates...

Homework Statement Let the time evolution of a system be determined by the following Hamiltonian: $$\hat{H} = \gamma B \hat{L}_y$$ and let the system at t=0 be described by the wave function ##\psi(x,y,z) = D \exp(-r/a)x,## where ##r## is the distance from the origin in spherical polars. Find...

Homework Statement Let ##\Psi(x,0)## be the wavefunction at t=0 described by ##\Psi(x,0) = \frac{1}{\sqrt{2}}\left(u_1(x) + u_2(x)\right)##, where the ##u_i## is the ##ith## eigenstate of the Hamiltonian for the 1-D infinite potential well. The energy of the system is measured at some t -...

Homework Statement A two-level system is spanned by the orthonormal basis states |a_{1}> and |a_{2}> . The operators representing two particular observable quantities A and B are: \hat{A} = α(|a_{1}> <a_{1}| - |a_{2}> <a_{2}|) and \hat{B} = β(|a_{1}> <a_{2}| + |a_{2}> <a_{1}|) a) The state...

Hi, I haven't posted for a while. I've seen this topic come up a few times, but it always seems to me that a few points aren't made clear. Can I just check the following is true? 1) The state space of a quantum system is always an infinite-dimensional seperable Hilbert space i.e. a Hilbert...

Homework Statement A two state system has the following hamiltonian H=E \left( \begin{array}{cc} 0 & 1 \\ 1 & 0 \end{array} \right) The state at t = 0 is given to be \psi(0)=\left( \begin{array}{cc} 0 \\ 1 \end{array} \right) • Find Ψ(t). • What is...

I am reading the book Introduction to Quantum Mechanics by David Griffiths and have come to the section on Dirac notation. It explains that the state of a quantum system is represented by a vector |β(t)> living out in Hilbert space, and, as with any vector, is independent of the choice of basis...

Homework Statement |O> = k |R1> + 1/9 |R2> a) Find k if |O> has already been normalized, and b) then the expectation value. The Attempt at a Solution a) To Normalise: |(|O>)|2 = (1/9 |R2> + k |R1>).(1/9 |R2> - k|R1>) = 1/81|R2>2 - k2|R1>2 = 1 I just assumed that |k| = (1-(1/81))0.5, but...

Homework Statement Quantum system in state |\psi\rangle. Energy of state measured at time t: Calculate probability that measurement will be E_{1}. Homework Equations |\psi\rangle=|1\rangle+i|2\rangle |1\rangle is normalised stationary state with energy E_{1}. Similarly with 2...

When you attempt to measure the motion a neutrino or a photon, one of the two subatomic particles being a massless particle and the other particle being a ghost particle, how would either of the two particles interact in a quantum state if both particles don't posses an inherent mass? I know...

Suppose we are given an arbitrary multi-particle quantum system whose state function / probability density does not change with time. Given, Einstein’s definition of time, that “time is what a clock measures”, is it possible to build a “clock” within such a system? More generally, does time...

http://arxiv.org/abs/0909.4321 Experimental Demonstration of a Robust and Scalable Flux Qubit R. Harris, J. Johansson, A.J. Berkley, M.W. Johnson, T. Lanting, Siyuan Han, P. Bunyk, E. Ladizinsky, T. Oh, I. Perminov, E. Tolkacheva, S. Uchaikin, E. Chapple, C. Enderud, C. Rich, M. Thom, J. Wang...

ground states Homework Statement Is it generally true that the ground state of a given quantum system corresponds to the lowest quantum numbers? For instance, is it generally true that the ground state of a system governed by a radial potential always corresponds to l=0? If not, how do we...

OK, let's say we have solved Schrodinger's eqn. for a system composed of a large number of degrees of freedom. We then start the wave-function off in an eigenstate of the nth energy level. It will never equilibrate- because the eigenstate is a stationary solution to S.E. Even if we use an...

After making a measurement of a particular dynamical variable the wavefunction collapses into the corresponding eigenfunction. As I understand when the variable is then measured again the results and relative probabilities of eigenvalues are exactly the same as before. I don't understand why...