What is quantum system: Definition and 39 Discussions

Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles.: 1.1  It is the foundation of all quantum physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science.
Classical physics, the collection of theories that existed before the advent of quantum mechanics, describes many aspects of nature at an ordinary (macroscopic) scale, but is not sufficient for describing them at small (atomic and subatomic) scales. Most theories in classical physics can be derived from quantum mechanics as an approximation valid at large (macroscopic) scale.Quantum mechanics differs from classical physics in that energy, momentum, angular momentum, and other quantities of a bound system are restricted to discrete values (quantization); objects have characteristics of both particles and waves (wave–particle duality); and there are limits to how accurately the value of a physical quantity can be predicted prior to its measurement, given a complete set of initial conditions (the uncertainty principle).
Quantum mechanics arose gradually from theories to explain observations that could not be reconciled with classical physics, such as Max Planck's solution in 1900 to the black-body radiation problem, and the correspondence between energy and frequency in Albert Einstein's 1905 paper, which explained the photoelectric effect. These early attempts to understand microscopic phenomena, now known as the "old quantum theory", led to the full development of quantum mechanics in the mid-1920s by Niels Bohr, Erwin Schrödinger, Werner Heisenberg, Max Born, Paul Dirac and others. The modern theory is formulated in various specially developed mathematical formalisms. In one of them, a mathematical entity called the wave function provides information, in the form of probability amplitudes, about what measurements of a particle's energy, momentum, and other physical properties may yield.

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  1. D

    I Gauge and Phase Symmetries in Quantum Systems: Exploring the Confusion

    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...
  2. E

    Details regarding the high temperature limit of the partition function

    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...
  3. A

    I Repeated measurements on a quantum system interacting with other quantum systems

    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...
  4. Lynch101

    I Rigorous: Where is the Quantum System Prior to Measurement?

    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...
  5. Lynch101

    I Where is the quantum system prior to measurement?

    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...
  6. AlexTab

    Finding the Ratio of Particles in a Three-Level Quantum System

    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...
  7. M

    I Can a quantum system with internal memory be in an energy eigenstate?

    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...
  8. S

    I How could a quantum system "predict the future"?

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

    Five State Quantum System, understanding the question

    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?
  10. S

    A Dipole moment of an isolated quantum system

    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
  11. C

    B Treating a galaxy as a quantum system

    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?
  12. DrClaude

    Two-level quantum system (from Sakurai)

    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...
  13. L

    A Can disjoint states be relevant for the same quantum system?

    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...
  14. Erland

    I Why does a quantum system with many degrees of freedom imply orthogonality?

    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...
  15. VSayantan

    Free Energy of a Simple Quantum System

    Homework Statement [/B]A quantum system has three energy levels, ##-0.12 ~\rm{eV}##, ##-0.20 ~\rm{eV}## and ##-0.44 ~\rm{eV}## respectively. Three electrons are distributed among these three levels. At a temperature of ##1727^o \rm{C}## the system has total energy ##-0.68 ~\rm{eV}##. What is...
  16. G

    Entropy of a generalised two-state quantum system

    Hi. This is the problem I'm trying to solve: A system may be in two quantum states with energies '0' and 'e'. The states' degenerescences are g1 and g2, respectively. Find the entropy S as a function of the Energy E in the limit where the number of particles N is very large. Analyse this...
  17. J

    I Question for large quantum system

    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...
  18. whatisgoingon

    Matrix representation of a quantum system

    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...
  19. B3NR4Y

    Two-Level Quantum System, Need help Finding State at time t

    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...
  20. N

    I A quantum system under constant observation

    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...
  21. Raptor112

    A Liouville Master Equation for an Open Quantum System

    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...
  22. B

    How to get the conserved quantities of a integrable quantum system?

    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!
  23. M

    Quantum system time evolution

    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...
  24. L

    Time-evolution of a quantum system

    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...
  25. C

    Time evolution of a quantum system

    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...
  26. C

    Expectation value of energy for a quantum system

    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 -...
  27. C

    Two-level quantum system observable quantities

    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...
  28. J

    The dimensionality of the state space of a quantum system

    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...
  29. B

    Two State Quantum System with a given Hamiltonian

    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...
  30. E

    Representing the state of a quantum system in different bases

    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...
  31. V

    Mass & Charge Distribution analysis in quantum system

    Pls. share all references about this. I found an interesting paper about mass and charge distribution analysis in quantum system. The paper conclusion is, Many Worlds and de Broglie-Bohm mechanics are falsified. Interesting (do you agree?): from the ADVANCES IN QUANTUM THEORY: Proceedings of...
  32. T

    Quantum System: Expectation Value

    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...
  33. A

    Calculating Probability of Energy Measurement in Quantum Systems

    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...
  34. N

    How would a photon or neutrino interact within a quantum system? Wh

    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...
  35. LarryS

    Time in a Steady-State Quantum System

    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...
  36. MTd2

    128 Quantum System D-Wave System on arxiv.org

    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...
  37. L

    Ground State of Quantum System: l=0?

    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...
  38. C

    Thermal equilibration of a quantum system

    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...
  39. S

    Remeasurement of a quantum system

    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...