Energy definition

1. Jan 25, 2007

xboy

How is energy defined in quantum mechanics?is it defined by the De-Broglie relations or from the eigenvalue equation of H operator?Are the two somehow equivalent?

2. Jan 25, 2007

dextercioby

Interesting question. Actually we have the energy observable (that is what is measured) and the Hamilton operator. If we measure the energy of a quantum system we should get a value from the operator's spectrum.

The measurement problem is really tricky and under debate, but energy is always associted to the hamiltonian.

3. Jan 25, 2007

xboy

What is the status of the De-Broglie relations then?Is it a derived result or an axiom?does it always hold?

4. Jan 25, 2007

Manchot

It is derived. It doesn't always hold, because it really only applies to particles in free space. If there is a non-constant potential present, then you cannot necessarily even assign a single "wavelength" to the eigenstates (only a spectrum of them). For example, the Hydrogen atom's ground state is exponentially decaying with radius.

5. Jan 25, 2007

xboy

so the de-broglie relation holds only for constant potential,is that what you are saying?what is the definiton of energy then?

6. Jan 25, 2007

StatMechGuy

Let me turn this around a bit -- what do you think the definition of energy in classical mechanics is?

7. Jan 25, 2007

xboy

ummm...a quantity that remains conserved because the lagrangian is time-independent?
can anyone please give me a sort of outline how i can derive the De-broglie relation for energy ?