an operator. The "application" of the operator on a differentiable wave function is as follows: p ^ ψ = − i ℏ ∂ ψ ∂ x {\displaystyle {\hat {p}}\psi =-i\hbar...
14 KB (2,071 words) - 14:44, 24 August 2024
T_{h}:=\left\{\psi \in L^{2}(X,\mu )\;|\;h\psi \in L^{2}(X,\mu )\right\},} is called a multiplication operator. Any multiplication operator is a self-adjoint...
48 KB (8,052 words) - 03:30, 27 September 2024
=p_{y}\psi \\{\hat {p}}_{z}\psi &=-i\hbar {\frac {\partial }{\partial z}}\psi =p_{z}\psi \\\end{aligned}}\,\!} Bounded linear operator Representation theory...
27 KB (3,587 words) - 12:55, 21 July 2024
that the lowering operator possesses a nontrivial kernel: a ψ 0 = 0 {\displaystyle a\,\psi _{0}=0} with ψ 0 ≠ 0 {\displaystyle \psi _{0}\neq 0} . Applying...
25 KB (4,461 words) - 00:10, 27 June 2024
{\displaystyle \psi } . Or more simply: The operator X {\displaystyle X} multiplies any wave-function ψ {\displaystyle \psi } by the coordinate function x {\displaystyle...
18 KB (3,125 words) - 04:12, 8 September 2024
Hamiltonian (quantum mechanics) (redirect from Hamiltonian Operator)
) ⟩ . {\displaystyle \left|\psi (t)\right\rangle =e^{-iHt/\hbar }\left|\psi (0)\right\rangle .} The exponential operator on the right hand side of the...
27 KB (4,903 words) - 04:26, 29 August 2024
displacement operator as D ^ ψ ( α ) = exp ( α A ^ ψ † − α ∗ A ^ ψ ) {\displaystyle {\hat {D}}_{\psi }(\alpha )=\exp \left(\alpha {\hat {A}}_{\psi }^{\dagger...
4 KB (725 words) - 04:59, 3 October 2022
angular momentum operator is one of several related operators analogous to classical angular momentum. The angular momentum operator plays a central role...
48 KB (7,596 words) - 22:03, 13 September 2024
Density matrix (redirect from Density operator)
This makes the operator ρ = tr 2 | Ψ ⟩ ⟨ Ψ | {\displaystyle \rho =\operatorname {tr} _{2}\left|\Psi \right\rangle \left\langle \Psi \right|} a convenient...
36 KB (5,247 words) - 07:41, 28 September 2024
translation operator determines is based on position-space wavefunctions. If a particle has a position-space wavefunction ψ ( r ) {\displaystyle \psi (\mathbf...
31 KB (5,662 words) - 11:32, 18 May 2024