# H(t1+t2) = Ht1+Ht2

1. Jan 3, 2010

### Cosmossos

Hello,
Is it correct to say that H(t1+t2)=Ht1+Ht2? I think it's true but I can't say exacly why.
And also, is it true that Ht2*Ht1-Ht1*Ht2=0?
would the answer change if we know the operator is harmitian or not?
Do you have any idea where can I find a summary about operators ?

Thanks

2. Jan 3, 2010

### blkqi

Re: Operators

An operator which commutes under addition and subtraction is called a linear operator, i.e. H is linear iff

H(t1+t2)=Ht1+Ht2, and
H(ct)=c(Ht).

It can be shown that every Hermitian operator is linear and commutes with itself ( [H,H]=0 ).

If you don't know the operator is Hermitian, or linear, then the commutativity requires proof.

Search wolfram mathworld for more info, http://mathworld.wolfram.com/LinearOperator.html

Last edited: Jan 3, 2010
3. Jan 3, 2010

### Fredrik

Staff Emeritus
Re: Operators

Are the t's vectors? Is H(t) supposed to be a time-dependent (Heisenberg picture) operator? If it's the latter, use A(t)=exp(iHt)A exp(-iHt).

I suggest you check out this book, but almost any book on QM or linear algebra will do.

Last edited: Jan 3, 2010