Functions of Operators

Examples

  • expaA=iAii!A

Theorem - Taylor Expansion

If F(A) is a Linear Operator then you can always Taylor Expand F(A).

Theorem - Commutations

If [A,B]=0 then [F(A),B]=0.

Theorem - Adjoint

(F(A))=F(A).

Corollary

If F is real and A is Hermitian, then F(A) is Hermitian.

Theorem - Eigenfunction

F(A)|ψ=F(a)|ψ.

Examples

exp(1iHt)|φn=exp(1iEnt)|φn.

Author: Christian Cunningham

Created: 2024-05-30 Thu 21:16

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