Examples of using Wavefunction in English and their translations into Vietnamese
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This feature of mathematics is known as wavefunction collapse.
The Hartree-Fock electronic wavefunction is then the Slater determinant constructed out of these orbitals.
Einstein could notaccept an interpretation in which the principal object of the representation- the wavefunction- is not"real.".
Is the state represented by the wavefunction ψ n ℓ m{\displaystyle\psi_{n\ell m}}.
However, various approximations, such as the Hartree- Fock method,can be used to estimate the ground state energy and wavefunction of the atom.
Additionally, these wavefunctions are normalized(i.e., the integral of their modulus square equals 1) and orthogonal.
By setting Z=1(for one proton), the normalized position wavefunctions, given in spherical coordinates are.
In C- H, some solutions to the Schrödinger Equation are shown, where the horizontal axis is position, and the vertical axis is the real part(blue)or imaginary part(red) of the wavefunction.
After we perform the measurement, obtaining some result x, the wavefunction collapses into a position eigenstate centered at x.
The wavefunction obtained by fixing the parameters to such values is then an approximation to the ground state wavefunction, and the expectation value of the energy in that state is an upper bound to the ground state energy.
After the measurement is performed,having obtained some result x, the wavefunction collapses into a position eigenstate centered at x.
The electron wavefunction spreads in a semiconductor lattice and negligibly interacts with the valence band electrons, so it can be treated in the single particle formalism, by replacing its mass with the effective mass tensor.
But how and why does measuring a particle make its wavefunction collapse, producing the concrete reality that we perceive to exist?
The particle actually has a range of values for all the properties, until you experimentally measure one of them- its location, for example-at which point the particle's wavefunction“collapses” and it adopts just one location.
However, if one measures the observable, the wavefunction will instantaneously be an eigenstate(or“generalized” eigenstate) of that observable.
The Hartree-Fock method accounted for exchange statistics of single particle electron wavefunctions, but not for their Coulomb interaction.
Most methods aim at computing the ground state wavefunction of the system, with the exception of path integral Monte Carlo and finite-temperature auxiliary field Monte Carlo, which calculate the density matrix.
Black lines occur in each but the first orbital: these are the nodes of the wavefunction, i.e. where the probability density is zero.
More recent variations of such antirealist interpretations suggest that the wavefunction is simply a way of"coding" our experience, or our subjective beliefs derived from our experience of the physics, allowing us to use what we have learned in the past to predict the future.
The most commonly described case, sometimes called the Aharonov- Bohm solenoid effect, takes place when the wave function of a charged particle passing around a long solenoid experiences a phase shift as a result of the enclosed magnetic field, despite the magnetic field being negligible in the region through which the particle passes andthe particle's wavefunction being negligible inside the solenoid.
Interpretations of quantum mechanics havebeen formulated to do away with the concept of"wavefunction collapse"; see, for example, the relative state interpretation.
For example,- even apparently simple problems,such as calculating the wavefunction of an electron orbiting an atom in a strong electric field(Stark effect), may require great effort to formulate a practical algorithm(if one can be found); other cruder or brute-force techniques, such as graphical methods or root finding, may be required.
Though this interpretation does mean that thequantum state of every particle in the universe affects the wavefunction of every other particle, it does so in a way that is only mathematical.
Their broadly antirealist"Copenhagen interpretation"- denying that the wavefunction represents the real physical state of a quantum system- quickly became the dominant way of thinking about quantum mechanics.
In addition to mathematical expressions for total angular momentum andangular momentum projection of wavefunctions, an expression for the radial dependence of the wave functions must be found.
The time evolution of wave functions is deterministic in the sense that- given a wavefunction at an initial time- it makes a definite prediction of what the wavefunction will be at any later time.
The basic idea is that when a quantum systeminteracts with a measuring apparatus, their respective wavefunctions become entangled, so that the original quantum system ceases to exist as an independent entity.
Where| n, ℓ, m⟩{\displaystyle|n,\ell,m\rangle}is the state represented by the wavefunction ψ n ℓ m{\displaystyle\psi_{n\ell m}} in Dirac notation, and δ{\displaystyle\delta} is the Kronecker delta function.[9].
The variational theorem states that for a time-independent Hamiltonian operator, any trial wavefunction will have an energy expectation value that is greater than or equal to the true ground state wavefunction corresponding to the given Hamiltonian.