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[tex]U=e^{iH}

[/tex]

where H is an operator.

1. If

[tex]H= \left(\begin{array}{cc}a & b\\c & d\end{array}\right)[/tex]

in its matrix representation. Then what is U in its matrix representation.

Im confused, is it

[tex]U= \left(\begin{array}{cc}e^{iH(1,1)} & e^{iH(1,2)} \\e^{iH(2,1)} & e^{iH(2,2)} \end{array}\right)[/tex]

where H(i,j) is the elements in H's matrix?

2. The hermitian adjoint of U is

[tex]U^+=e^{-iH^+}

[/tex]?

(+ represents hermitian adjoint...couldnt find the correct symbol)

2b. In matrix form the hermitian adjoint is the complex conjugate transposed?

2.c In operator form ? lets say H=i*f(x) then

[tex]H^+=-i*f(x)

[/tex]

?

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# Homework Help: Help with math operators

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