In plain English, what is Hermitian Operator in Quantum Mechanics?

Question

I hear it so much, but I have no idea what it actually is!

In my notes, it says "a matrix with real eigenvalues", but this confuses me further. Perhaps I'm slow?

Answer 1

I think its a square matrix with the property such if the diagonals are transposed it leads to [H][H*]=n[H]
in heisenbergs matrix formulation of quantum mechanics, the energy of a quantum system could be obtained by operating (measuring) with the Hamiltonian matrix which fulfilled the necessary hermitian conditions.
Things get a bit simpler if you consider the Schrodinger wave formulation, where after dirac's lambda= h/p for particle wavelength you can build up a wave equation for a given particle configuration. It's of the form
(h^2/2m )*grad^2(phi)+ (E-V)*(phi)=0
If you use the hamiltonian operator on this function (H=i*h*d(phi)/dt.)..you end up with a general equation..H(phi)=E(phi)

Answer 2

Real eigenvalues are mathematical derivatives. But the Quantum mechanics itself I found to be 50% fiction. So you don't really know which avenue you are heading. I will wait a few more years. This years stuff is out of print next year. There are too many unemployed scientists on the Afghan for QM to be of value at the moment. Get Harry Porter.

Answer 3

You are doomed.
If anyone can give a nice simple plain English description to either half of this question I would be most impressed ( and worth buying a free pint ).

Read the textbooks, if it does not make sense try a different textbook - that always worked for me.

Answer 4

It is a mathematics concept that does not lend itself to plain English. The most straight forward explanation is wikipedia under Hermitian.
http://en.wikipedia.org/wiki/Hermitian
Check out matrix and operator tags. The connection is that a Matrix is defined for a vector space with orthogonal basis vectors and QM operators are defined for a hilbert space of orthogonal basis functions.

Answer 5

The best book I know in plain English is 'The Dancing Wu Li Masters' i think it's by Gary Zukav, I read it some time ago. Hope you find your answer!

Answer 6

To put it in plain English, Hermitian Operator is a distant relative of Herman Munster. He's a Mechanic who had a tragic accident and ended up with a bolt through his neck.

Hope this helps.

Answer 7

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