Hamiltonian vs. Hermitian

  • Thread starter piareround
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  • #1
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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)" [Broken], 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?
 
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  • #2
tom.stoer
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"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 :-)
 
  • #3
dextercioby
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'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>.
 
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  • #4
tom.stoer
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... 'hermitean' is misleading. In ... quantum physics we should use <symmetric> and <self-adjoint>.
I fully agree!
 
  • #5
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In finite spaces Hermitian works fine, but I agree that for infinite dimensional spaces self-adjoint is the better term.
 
  • #6
Pengwuino
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Also, the Hamiltonian is a concept that extends from Classical Mechanics. It is not unique to quantum mechanics
 

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