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...

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...

=p_{y}\psi \\{\hat {p}}_{z}\psi &=-i\hbar {\frac {\partial }{\partial z}}\psi =p_{z}\psi \\\end{aligned}}\,\!} Bounded linear operator Representation theory...

\quad \forall \psi \in L^{2}.} That is, the position operator X {\displaystyle X} multiplies any wave-function ψ {\displaystyle \psi } by the coordinate...

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...

) ⟩ . {\displaystyle \left|\psi (t)\right\rangle =e^{-iHt/\hbar }\left|\psi (0)\right\rangle .} The exponential operator on the right hand side of the...

operator is sometimes called the creation operator, and the lowering operator the annihilation operator. Well-known applications of ladder operators in...

angular momentum operator is one of several related operators analogous to classical angular momentum. The angular momentum operator plays a central role...

translation operator determines is based on position-space wavefunctions. If a particle has a position-space wavefunction ψ ( r ) {\displaystyle \psi (\mathbf...

This makes the operator ρ = tr 2 ⁡ | Ψ ⟩ ⟨ Ψ | {\displaystyle \rho =\operatorname {tr} _{2}\left|\Psi \right\rangle \left\langle \Psi \right|} a convenient...