What Is the Difference Between Hamiltonian and Hermitian Operators?

[piareround]

If anyone has time could they please answer this question.


I was looking and concept of the the http://en.wikipedia.org/wiki/Hamiltonian_(quantum_mechanics)" , I was wonder is their a difference between the two terms? If so how are Hermitian and the Hamiltonian different? Can anyone give an example?

 

[tom.stoer]

"hermitian" is a general mathematical property which apples to a huge class of operators, whereas a "Hamiltonian" is a specific operator in quantum mechanics encoding the dynamics (time evolution, energy spectrum) of a qm system.

The difference should be clear.

A Hamiltonian must be hermitian, whereas not every hermitian operator is a Hamiltonian.

(the number 17 is positive number, but not every positive number is equal to 17 :-)

 

[dextercioby]

'Hamiltonian' is also an adjective :-) (pertaining to Hamilton ?)

On a serious note, 'hermitean' is misleading. In the mathematics of quantum physics we should use <symmetric> and <self-adjoint>.

 

[tom.stoer]

... 'hermitean' is misleading. In ... quantum physics we should use <symmetric> and <self-adjoint>.

I fully agree!

 

[dpackard]

In finite spaces Hermitian works fine, but I agree that for infinite dimensional spaces self-adjoint is the better term.

 

[Pengwuino]

Also, the Hamiltonian is a concept that extends from Classical Mechanics. It is not unique to quantum mechanics