Search results
Results from the WOW.Com Content Network
The corresponding eigenvalue, characteristic value, or characteristic root is the multiplying factor ... from geology to quantum mechanics. In particular, ...
An eigenvalue is said to be non-degenerate if its eigenspace is one-dimensional. The eigenvalues of the matrices representing physical observables in quantum mechanics give the measurable values of these observables while the eigenstates corresponding to these eigenvalues give the possible states in which the system may be found, upon ...
In quantum mechanics, a complete set of commuting observables (CSCO) is a set of commuting operators whose common eigenvectors can be used as a basis to express any quantum state. In the case of operators with discrete spectra, a CSCO is a set of commuting observables whose simultaneous eigenspaces span the Hilbert space and are linearly ...
Since the angular momenta are quantum operators, they cannot be drawn as vectors like in classical mechanics. Nevertheless, it is common to depict them heuristically in this way. Depicted on the right is a set of states with quantum numbers ℓ = 2 {\displaystyle \ell =2} , and m ℓ = − 2 , − 1 , 0 , 1 , 2 {\displaystyle m_{\ell }=-2,-1,0 ...
In quantum mechanics, the position operator is the operator that corresponds to the position observable of a particle.. When the position operator is considered with a wide enough domain (e.g. the space of tempered distributions), its eigenvalues are the possible position vectors of the particle.
In quantum mechanics, the Hamiltonian of a system is an operator corresponding to the total energy of that system, including both kinetic energy and potential energy.Its spectrum, the system's energy spectrum or its set of energy eigenvalues, is the set of possible outcomes obtainable from a measurement of the system's total energy.
In quantum mechanics, observables manifest as self-adjoint operators on a separable complex Hilbert space representing the quantum state space. [1] Observables assign values to outcomes of particular measurements, corresponding to the eigenvalue of the operator.
If the operator acts on a (normalizable) quantum state then the operator is self-adjoint. In physics the term Hermitian often refers to both symmetric and self-adjoint operators. [7] [8] (In certain artificial situations, such as the quantum states on the semi-infinite interval [0, ∞), there is no way to make the momentum operator Hermitian. [9]